Where I beaver trap (a mix of ponds, streams, lakes and big rivers ), I’m using 1/8 cable sliders that are made up 10 feet long. You can always anchor higher on the shoreline if you don’t need the extra length. You could do the same with a piece of 8 foot rerod. With rare exception, I wouldn’t consider anything shorter than 8 foot to get a beaver into drowning depth water.
I agree totally with BB. We use 10' lengths of rebar and also wouldn't go less than 8' to ensure getting out to drowning depth. Remember you'll have to stick 1-2 ft. in the mud to anchor under water then have 1 ft. or more anchored out of the water.