I assume you mean a 7.62 rifle round. The only indoor ranges that I have heard you can fire centerfire rifle ammo is I think Blue Plains and the NRA ranges in Virginia. As far as outdoor ranges go, there is the private club in Bowie called Berwyn Rod and Gun Club.
Depending on where you live, there is also a public park range in or around La Plata that is an outdoor range you can shoot at for a small fee, and I keep hearing about some range in AA Co that is mostly pistol but allows rifles on some days or something like that, but I have never been there.
Edit: I forgot, there is also the private St. Charles Sportsman Club just outside of Waldorf.
Addendum to the edit: The range in or around La Plata is Myrtle Grove and here is a list of some ranges around the area the DNR compiled http://www.dnr.state.md.us/wildlife/shootingranges.asp
It is not a complete list of all ranges by a long shot, but it is a start.
I know they're still rebuilding the Hap Baker range, but do they allow these rounds? I called this one range and they told me that they would take the British .303 round at Hap Baker.