Bicycling and a Right Turn Only Lane?
The key thing, is that you never want to be to the right of cars that are turning right.

Depending on the exact lane setup and traffic amounts, I would do one of these:


Merge left into the go-straight (left) lane, so that anybody turning right is in a separate lane to the right of me.
Be in the center or left third of the right-turn lane, so that anybody turning right is blocked by me and has to wait for me to get into the intersection
Split the lane, riding in between the left and right lanes.


Exactly which I actually do depends on the traffic levels and what the far side of the intersection looks like. I would only do the 2nd or 3rd options if right-turning traffic is low and there's clearly space on the far side of the intersection for me to be to the right of the going-straight traffic (2 lanes, or 1 lane with a bike lane or wide shoulder).

To repeat: the main thing is to not be to the right of cars turning right. Get to their left or directly in front of them.