For example, according to Six Flags Magic Mountain's website, guests are not permitted to ride any rides with a hard cast or splint. However, for rides that do not require riders to be restrained by an over-the-shoulder harness or a lap bar, guests may ride with a soft cast, such as an ACE wrap, as long as it does not impair the safe operation of the ride.
It is always best to check with the specific amusement park and ride in question to determine their policies and restrictions regarding riding with a splint on.