Hi Michael,
I'm afraid that, unless you created a backup of that file geodatabase on your system somewhere, there is not a way to recover that deleted field. I presume you were in an edit session? Choosing not to save your edits and ending the session would be the only way to revert back to where you were before deleting.
You might check with your IT department and see if they have a backup of the drive where that file geodatabase resided and maybe you can pull an older copy from there?
Good luck!
Jonathan