The only Golf Course my husband played that required proof of handicap was St. Andrews Old Course. The handicap required for men was 24. My husband can not remember what the required handicap for women was. St. Andrews has several courses, the others may not require a card.
Since he was a single he rarely had trouble getting on any of the courses. At St. Andrews Old Course, he got to the course a 6:30am, put his name on a waiting list and was placed with a group by 8:30am.
The other courses he played were Cruden Bay, Royal Aberdeen. We looked at Carnoustie, Troon and Turnberry but due to time considerations were unable to play. If you have interest in any of the above courses let me know and I will try to pry information from my husband.
This web site may help:
www.scotlands-golf-courses.com