It will fit but isn't what you need. The cheek rest for the M1 Garand was made to set the cheek more to the left. This helped line the eye up with the offset scope mounted on the Garand.
The M1A mounts over the bore line and your cheek needs to be raised up instead of over. There are numerous manufacturers out there making a similar product to raise the cheek. I think Blackhawk industries makes some and I'm sure others do as well.
Tried ones from Blackhawk / Eagle as well. Disappointed in them too.
The best, by far, is a rigid adjustable cheek rest. I wasn't the biggest fan of the M3A type at first, but it's grown on me. Except for the rubber mouse pad type neoprene coat. That needs to be redone.