Wiggle position will work on any layer, even a text layer. The layer will wiggle for as long as the layer lasts.
If you want to create a short clip with a wiggle that will seamlessly loop then you need to do a bit more work. If that is what you want the easiest solution is to pick the length of the clip you want to loop first, add your text layer, apply a wiggle expression that gives you pretty much what you want, then use the Keyframe Assistant to convert the expression to keyframes, then apply the smoother to reduce the number of keyframes and put some nice motion curves on the motion, then copy the first position keyframe, move to the end of the timeline and paste the first keyframe there. If there is another keyframe very close to the last keyframe delete that. Now run a ram preview and see if you get the kind of a wiggle you want. If you do, then grab the last keyframe and move it one frame to the right, render the comp. You can now loop that footage forever and the loop will be seamless. This is often useful if you need looping motion in an edit because you can loop footage in Premiere Pro and it won't take any extra time to render.