Yes, but I replaced my entire fitting.
Which bulb you have depends on the year of your boat, & which fittings you have.
I have a 1977 boat, so I have the old SeaDog fittings (teak pad,etc..)...Hence, I replaced my anchor light with the AquaSignal Series 20 (8" stick with screw in base) and put a BA-9 9-LED bulb in it from superbrightleds.com.
One of the issues with simply replacing the running lights & anchor light with LED bulbs is most replacement bulbs are NOT USCG approved (but there are a few, $$, see below). If the USCG wants to climb my rig and inspect my anchor light for compliance, they are welcome to...it is as bright as the 10w halogen bulb it replaced & has a 360 degree arc, but draws 35mA.
Additionally, unlike incandescent bulbs, you cannot simply put a white LED light behind a colored lens (i.e. running light). You must put a red LED behind the red lens and a green LED behind a green lens. That being said, there are a few LED fittings & replacement bulbs for running lights that are approved. Check out Dr. LED. (I think it is doctorLED.com)
I chose to keep the incandescent festoon in my new Series 25 steaming light (also replaced & re-wired while I had the stick down) since I figured I'd only have the steaming light on while motoring, so power draw should not be a concern. I also have the old OEM running lights in the hull. They still function, but I hope (someday) to add the bow pulpit style when I get around to it during the boat re-wiring project. I would expect I'd get the Dr. LED style bulbs for those fittings at that time.
Good luck.