Can I ask a Master's paper reader to be a referee for Ph.D.? I am applying for Ph.D. and am looking for a third referee. I was wondering if it is appropriate to ask a reader of my Master's paper? To be more specific, he was a post-doc at the time but since has earned a position at another university as Assistant Professor. He was not only one of the readers of my paper, but has seen me give a few seminars and knows me personally.

Any clarification on this matter would be greatly appreciated!
For sure it may depend on the rules your university has, but if the referee can explain the occasions in which he could assess you (in your case seminars and thesis), and why he thinks you would be a good candidate, I do not see any problems in asking him.
The fact that he is now a professor (even if somewhere else) is only a plus.