Robert Maxwell (12 May 1876 – 25 July 1949) was a Scottish amateur golfer who played during the late 19th century and early 20th century. Maxwell had four top-10 finishes in The Open Championship. His best performance came in the 1902 Open Championship when he placed fourth. Maxwell won The Amateur Championship twice, in 1903 and 1909, both events having been played at Muirfield.

Maxwell was born in Edinburgh, Scotland, on 12 May 1876. He was the son of Francis Maxwell and Adelaide Maxwell (née Hay). At age four, he was living in North Berwick, Scotland with his parents, two brothers, and a sister. He received his education at Eton College and was an energetic boy. While at Eton, he acquired a "short and concise" manner of speaking.

As a youth, he was adroit at football and rowing. By age seven, Maxwell had already honed his golf game and, thanks to golf lessons he had received from Ben Sayers, the precocious young lad carded a 74 in two rounds on the Ladies' Course at North Berwick. As a young man, he had powerful arms and wrists, a quick swing, and was a long hitter of the golf ball.

In 1909, Walter Travis, editor of The American Golfer magazine, described Maxwell as "... a big, tall, powerful man with massive proportions and a fine pair of legs under him. His style is rather forceful, and perhaps, as some would say, a trifle clumsy. He hits hard, but unlike many other hard hitters he is most wonderfully accurate. He employs an open stance ... and uses the Vardon grip with his right thumb down the shaft. With his irons he is wonderfully accurate ... and he uses an iron putter—and his style does not look as if it would make for delicacy, but he has an extraordinarily fine touch, and as a matter of fact he was about the best putter there was at Muirfield, hardly ever missing a short one."

Maxwell, the upstart youngster, first entered the Amateur Championship when he was only 21 years old. He made news in the 1897 tournament at Muirfield by beating John Ball, the 4-time (and later 8-time) Amateur champion, and also knocked off Harold Hilton.

In his match against Ball, Maxwell stymied the great champion on three of the first eight holes, and eventually finished him off by the score of 6 & 4. Maxwell finally fell victim himself when James Robb beat him 1 up in the fifth round.

Known as "Bobbie" by his fans and those who knew him, Maxwell was skilled enough at golf by 1900 to begin winning tournaments. He notched three wins in the North Berwick club championship from 1902 to 1904. In 1903 he added the Amateur Championship to his list of tournament wins.

In total, he entered the British Amateur thirteen times and played in The Open Championship seven times between 1900 and 1909. Maxwell had nine caps for Scotland when he represented his country against England in international matches. In several of those matches he was paired against John Ball, crushing him on three occasions–once by 12 & 10 and twice by 8 & 6 margins of victory. He won the Glennie Medal at St Andrews three consecutive years from 1901 to 1903.