Either you make some sort of raft using SAK, fire and paracord or you just take almost all your clothes and shoes off, throw it across the river to the other side, jump in* and swim like Thorpe to get there.
Staying put won't work because it is not an option in this game .

*Maybe it would be good to take a dip first so you won't be in shock when you plunge into the cold water later.