Can I substitute yogurt for vegetable oil in a cake mix?

Try prune purée or applesauce.

No, unless you're prepared to accept results that are very different from, and probably greatly inferior to, what the cake mix maker intended. First, you'd be replacing an ingredient that is pure fat with one that's mostly water. Second, yogurt is a highly acidic ingredient; using it instead of oil will probably throw off the cake's leavening.