I've just sold my kitchen aid stand mixer before I move - is is possible to cream butter and sugar in a food processor?
You can do it by hand if the butter is really soft
I've made several cakes in a food processor. Instead of creaming the butter and sugar, I've whizzed the eggs and sugar, then added soft butter, then the dry ingredients. It has worked well for pound cakes and carrot cakes which I always make in the processor.
Food processors don't beat air into batter the way a mixer does, so the cake is likely to be heavier and denser.
Plevee's suggestion will work. You can make cakes very successfully in the food processor, but not the same way you'd do it with a mixer. Eggs and sugar first, then soft butter.