No you cant here is the rule:
Article 4 — Designated Quarterback
Prior to the game, a team is required to designate three players who shall be permitted to alternate for each other during the game at the Quarterback position exclusively. Not more than one such player may be in the game at any time and none of the three can enter the game as a member of Team B.
PENALTY: L25 PLS DR or L25 PBD or option.
NOTE: For the purposes of this Article 4, the duties of the Quarterback position may include punting, place kicking and kicking off. If a team designates three Quarterbacks for a game, the player designated as the third Quarterback shall not be eligible for kicking duties.
NOTE: A team is required to have one designated quarterback or kicker on the field for each of its offensive plays.