"Rota" is short for "rotation," and when the term is used in a golf context it refers to the golf courses that rotate as sites of a specific tournament.
Most professional tournaments are played at the same course each year, or at least change courses infrequently. But some rotate among a select group of courses. If the Anytown City Championship is played on Course A this year, Course B next year, Course C the year after that, and then the cycle repeats every three years, then Courses A, B and C make up the tournament's rota.
The term "rota" is most closely associated with the British Open, because the R&A, media and fans all use the term "Open rota" to refer to British Open host courses. See "What is the Open Rota?" for details on the courses included in that rota.
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Examples: "This is the best course in the tournament rota."
"I wish they'd add this course to the rota for the City Championship."