Implied yes, according to the movie
To supplement Valorum's excellent extended canon answer, we also know from the films that, at least according to Obi-Wan, Owen knew that Obi-Wan had fought in the Clone Wars, and believed that Anakin had followed Obi-Wan offworld on an "idealistic crusade:"
No, my father didn't fight in the
wars. He was a navigator on a spice
That's what your uncle told you. He
didn't hold with your father's ideals.
Thought he should have stayed here
and not gotten involved.
You fought in the Clone Wars?
Yes, I was once a Jedi Knight the
same as your father.
I have something here for you. Your
father wanted you to have this when
you were old enough, but your uncle
wouldn't allow it. He feared you
might follow old Obi-Wan on some
damned-fool idealistic crusade like
your father did.
From this, here's what we can infer that Owen knew:
- Obi-Wan wanted to give Luke a lightsaber
- Obi-Wan fought in the Clone Wars, with Anakin
- Obi-Wan led Anakin on an "idealistic crusade" (with the word choice of "crusade" having religious connotations)
Also, here's what it's implied Luke knew as common knowledge before this scene:
- The Jedi Knights fought in the Clone Wars (otherwise, "Yes, I was once a Jedi Knight" would be a non sequitur response)
This means that, unless Owen thought that non-Jedi recruited Jedi, fought in the Clone Wars alongside the clones, and would want to give Luke a lightsaber, he probably knew the truth.
That old man's just a crazy old
wizard. Tomorrow I want you to take
that R2 unit into Anchorhead and
have its memory flushed. That'll be
the end of it. It belongs to us now.
Owen himself calls Obi-Wan a "wizard", which is certainly an odd choice of words if he doesn't think he actually has any powers.