Electrical wire in the way of exhaust fan?

Perhaps you can place a shim between the joist and the fan to hold the fan off the joist by 3/4" or so. That way, the wire can remain untouched. Shims are commonly used for puposes such as this. They are just pieces of wood cut to the right size and tapped into place before final fastening.

pack out the joist with a small strip of wood etc to give the wire some clearance between it and the box...a 1/2" strip of plywood 3" by 12" long would probably do it. screw the plywood on then screw your fan to the plywood. watch you don't hit wire with screws. now your fan would be shifted a half inch out of center of your hole but if the cover attaches to the middle you should be good to go...

You have 2 basic chooses. You can move the fan far enough to avoid the wire, or you can move the wire enough to avoid the fan. The shims suggested by other answers sound like the best option.

Electric wires are stapled in place every 4', Just undo some staples to get some slack in the line and re staple it so it clears the fan housing.