James Rennie (c. 1826–1924) was a Scottish professional golfer who played in the late 19th century.

The 1875 Open Championship was the 15th Open Championship, held 10 September at Prestwick Golf Club in Prestwick, South Ayrshire, Scotland.

Willie Park, Sr. won the Championship by two strokes from runner-up Bob Martin.

Rennie had rounds of 61-59-57=177 and won £1 in prize money.

Note: Rennie played only in The Open Championship.