Assuming you mean no roll control at all, lateral weight shifting has an effect too mild to be able to achieve useable control.
However, most airplanes can be controlled in roll by yawing them, depending on how strong the design's dihedral effect and roll/yaw coupling is.
For example, high wing Cessnas that have geometric wing dihedral along with the T wing placement can get decent roll rates going just by skidding. I used to tow gliders in a Cessna L-19 and I could control the plane reasonably well just with trim for pitch, and rudder for roll, without touching the stick at all, and I could probably land it in one piece, or at least walk away from the result, using trim and rudder only, if the runway was long enough.
Swept wing jets have very strong dihedral effect from the wing sweep itself (so much that anhedral is required if the wing is on top, to reduce total dihedral effect). If you lose all aileron control in a swept wing jet you can get very high roll rates going with small amounts of rudder-induced skid. As long as the yaw damper is still working so you don't have to struggle against dutch roll tendency, you could maneuver a jet around with mild rudder inputs to skid it to roll it into a bank, if you were very careful, if you had no aileron control (I used to experiment with that in the CRJ simulator, just for fun).
Landing a jet on rudder alone, well I'd try it if I had no choice, but I'd probably crash it.