At least, not individually - an Ork horde has a soul, made up of the tiny little parts brought together by the Orks within it, and this manifests via the Weirdboy. This is why Weirdboys are more powerful in bigger Waaaghs (they have a 'bigger' and thus more powerful soul) and why only they explode when things go wrong.
I've heard the theory that this is because they are artificial lifeforms created by the Old Ones. Similar to the Tau, who are also blanks and VERY strongly implied to be the result of Eldar tinkering. Unlike the Tau, they were created as a 'warrior race and as such were given a few Psykers as an in-built weapon, of sorts.
This is an interesting theory but it struggles to explain the Eldar, who were also created by the Old Ones and are exclusively psykers. You could just say that the twos races were just designed that way, but that leaves me with the unfortunate conclusion that souls are not inherently valuable, if they can be given or taken away on such scale, and that contradicts a large portion of the canon regarding Psykers, the Fall, the appetites of the Chaos Gods and the Imperium.