On the day you get your contraceptive injection can you have sexual intercourse?

Sure: Sure you can have intercourse, however, a backup method of contraception would be recommended to be on the "safe" side in preventing conception from an egg that may have already been released.

Maybe: Whether or not you are protected from pregnancy the day you get the injection depends on a number of factors. If it is 5 days or less since your last period started, you are protected immediately. If it has been over 5 days since your last period started, you are not protected for 7 days. If this is not your first shot and you are getting it on time, you are protected immediately. Regards!