In a word, no. It’s not permitted to climb the sea stacks at Reynisdrangar. Not only is it very dangerous, but the rock formations are highly protected. Obviously, you’d need to hire a boat to climb them too.
Scrambling is not allowed at all on Reynisfjara in general. There have been fatalities on the beach caused by rogue waves, and it is simply not worth the risk. Please don’t do it.