The Rambler Tarpon was a concept car, a compact-sized sporty youth-oriented 2+2 hardtop coupé developed in 1963 by the Rambler Division of American Motors Corporation (AMC). The bright red with black roof design study made its public debut at the 1964 Chicago Auto Show. The car served to foretell the fastback design elements of the larger Rambler Marlin that was introduced in 1965.

The Tarpon was an "aquatically named" design study for a small rear-wheel drive two-door monocoque pillarless hardtop. Characteristic was its sleek, sloping fastback roof that narrowed as it met the rear bumper. The Tarpon featured two large, deep taillights flowing from the rear fender's shoulders. The show car was finished in red with a black vinyl roof accenting its clean shape from the windshield back to almost the rear bumper. The long roof portion design incorporated extended and sizeable rear quarter windows that ensured rear seat passengers in this 2+2 interior avoid claustrophobia. The smooth roofline was unbroken by the nearly horizontal rear window. Tarpon’s fastback design "was on the cutting edge of a Motor City styling trend that soon included the Plymouth Barracuda, the Mustang 2+2, and the Dodge Charger."

In a 1991 book about collectible cars, automotive historian Richard M. Langworth described the Tarpon's sweeping roofline and "roughly elliptical side window openings suited the American's handsome lines to a T, and the pretty well-proportioned fastback looked a natural for showroom sale." The upward line that was at the bottom of the rear-quarter windows to apparently break up their visual mass has been viewed as the "single weirdest quirk of the Tarpon". The show car also had no trunk lid or outside hatch to access the cargo area. This would be addressed before production.

The Tarpon concept "generated much excitement at the Society of Automotive Engineers (SAE International) convention in January 1964." The concept was shown with the designers worked on a cutaway profile of the car on stage. The Tarpon then generated broad public interest as it toured the auto show circuit starting in January 1964. Its semi-boat tail roof design was accented with black vinyl first appeared at the Chicago Auto Show. The sales pitch for the concept was "A new car with sports flair." It was well received at automobile shows before the so-called "pony car" market segment was established. Some show attendees wanted to place orders, AMC dealers asked about production plans, and "Over 60% said they'd like to own a model with the Tarpon's fastback styling."

The Rambler Tarpon was also on display at the 1964 New York International Auto Show, as well as the Ford Mustang II (concept car), a design shown shortly before the production version was unveiled. Both concepts were targeting the increasing interest in small, sporty cars, and the purchasing power of younger customers.

The automobile marketplace was changing in the early 1960s "when many young, first-time drivers entered the market ... and bought cars with flair." Early in 1963, American Motors' management began the development of "a new car with a sports flair" to modify its image. Dick Teague's styling team devised an entirely new concept for AMC - a fastback design. He had a passion for pre-World War II automobiles and had a "passion for taking old styling and making it new again." He observed the 1963 Chevrolet Corvette spit-window coupe design and the 1963 Ford Galaxie Sports Hardtop, which outsold the notchback models, followed the pattern set by Chevrolet's distinctive 1942 Fleetline two-door fastback body style called the Aerosedan and Nash's own Airflyte. Teague knew that his design team had to work with considerably smaller budgets than their counterparts at Detroit's Big Three (General Motors, Ford, and Chrysler). For example, Ford developed a handmade fastback roofline for its first-generation compact Falcon two-door sedan, named "Falcon Challenger III". The car was entered in the 1962 Nassau Speed Weeks and also displayed during the 1962 New York International Automobile Show. Ford also introduced semi-fastback designs for midyear 1963 featuring a lowered, sloping roofline along with a rear window to enhance aerodynamics. On the other hand, AMC did not have the corporate resources to undertake the significant investment that would require all-new tooling, so Teague's design team had to make imaginative use of existing tooling to create spin-offs from existing products.

The Tarpon was made on the compact-sized Rambler American's new design and platform already set for the 1964 model year. A convertible chassis was used 106 in (2,692 mm) wheelbase), but the Tarpon was slightly longer, 180 in (4,572 mm) compared to 177.25 in (4,502 mm) for the production Rambler American. The Tarpon's roof was lowered two inches making it only 52.5 in (1,334 mm) high for an even more dynamic look. The top section of the new Rambler Tarpon was made of reinforced plastic. The windshield was described as "bulbous" and the fastback roofline featuring a "skylight" rear window. The swept back, double-compound curved windshield further enhanced the Tarpon's low appearance. The Tarpon also featured polished 13-inch aluminum wheels. The standard production road wheels on Rambler Americans were 14-inch, so the smaller versions made the show car lower. The interior had a complete set of dial-type gauges under a padded dash, a deep-dish aluminum steering wheel rimmed in walnut, and custom bucket seats.

The Tarpon seemed to aim Plymouth's new Valiant-based Barracuda and the soon-to-be-announced Ford Mustang. Shown before the introduction of Ford's compact Falcon-based Mustang, AMC's Tarpon was "an instant success" as evidenced by surveyed potential buyers stating 60% would buy one.