It is the Captain's switch by tradition here.

In recent years there has been a movement on the MD-88 and some 737-800 bases toward the FO actuating the beacon. Some are doing it now as a matter of course without asking prior permission. It has caused a couple of crews to get in hot water with the beacon running and the airplane nowhere close to pushback, and it has caused some intra cockpit "CRM" discussion. In any case, as it's the pay switch, it's the Captain's call.