Piggy-backing off Andrew's answer, the word estrange can be used as a verb, but I don't hear it used that way very often, and it sounds awkward to me when I try to use it that way:
He estranged his brother last Christmas after an argument about politics.
You can look at this Google ngram and see that the adjective form has become much more popular than the verb form over several decades.
However, I looked up the verb estrange in the thesaurus, and found a very suitable synonym: alienate.
Unlike estrange, writers use alienate more often as a verb than as an adjective, according to the ngram. So you could say:
He alienated his brother last Christmas after an argument about politics.
According to NOAD, alienate is defined as:
alienate (verb) cause (someone) to feel isolated or estranged; cause (someone) to become unsympathetic or hostile
Looking up alienate in a thesaurus provides some other candidate verbs, such as divide (which is fairly common) and disunite (not so much so). However, I think divide works better in a more passive construct:
The brothers were divided last Christmas after an argument about politics.
(You wouldn't say, "He divided his brother last Christmas..." – at least, I hope the argument wouldn't get that out of hand.)