As GEddie notes, every living being has a principle of life, including animals and even plants, and this may rightly be called a “soul.” But assuming you mean immortal and rational souls, akin to what we have, that would simply depend on whether God willed to create them rational beings or mere animals. (Would plants on other planets count as “aliens”?)
It would certainly be possible for innocent beings to exist in a fallen universe without themselves being fallen–but as Farley4334 notes, they would be affected adversely in some way. Our Lady was conceived without original sin, but as a consequence of the fall she suffered in this world–though not without joy and merit. I don’t think Adam’s sin would be transmitted to aliens, because by definition the aliens would be a different line of beings with a different moral track record.
It is highly unlikely, however, that aliens exist, given all the precise conditions for organic life, which as far as we know are only met on this planet.