only if the phone was sold by AT&T in the first place. I was gonig to give my friend my old phone and it was AT&T and he had a T-Mobile SIM and it didn't fit. And it was a Razr so it's not like it was an exclusive to AT&T or anything.
If you have a network free Motorola phone means,you will be able to use your AT&T sim card.
Locked by specific network means,you will need to unlock your phone.For unlocking you can approach your service provider or else try to buy an unlocking service from any one of the online unlocking service provider like MobileUnlockSolutions.com Here you can unlock your phone at low cost.