Of course you must use the current to get you across - you just cannot fight it and win.

Various ferrying scenarios keep you / float/ raft, pointed toward the bank you want to reach by way of a paddle / sweep pole, and the current will force you / float / raft to the other shore. Angle control and stability difficulties are easy to imagine.

How about this:

At the waters edge, by lashing, build a semi-rigid "pole" of roughly harvested trees longer than the river is wide. Use as few trees as you can to minimize the number of lashings. "Hinge" the pole solidly at the downstream end with whatever you have or make. Make yourself as buoyant as possible to insulate your core as much as you can. Push off on the upstream end of the pole and the current will rapidly "close the door" by pushing the upstream end of the pole across the river - where you better get off pretty quickly before the river destroys the "door."