My father has MRSA and is on antibiotics. Can he hold my newborn baby in the hospital?

Yes. Use gloves and wash your hands before putting on the gloves. Some hospitals also, require paper gowns. Minimal contact is best while the baby is so young.
No. Too risky. Baby may get colonized. Have to take all the precautions, if he really wants to hold the baby.
MRSA + Newborn. I would be very cautious about anyone with a MRSA strain holding a newborn. For the first few months of life, the infant has a sort of congenital immunity. However, MRSA can be a dangerous and invasive bacteria which would require some powerful medications, some of which could pose risks to the newborn. I would discourage him from holding the baby, discuss this with pediatrician and neonatologist.