More generally, is there any compelling evidence for any common roots between early Indo-European and Afro-Asiatic languages? There are almost necessarily some words that are not too dissimilar phonetically, and relatively similar semantically, but there's no particular reason to believe that such are more than coincidences. (I just bumped into the pair pecca/pesha' (פֶּשַׁע), both meaning "sin" as an example of likely coincidental resemblance and asked an earlier question on an even less likely pair).
The most common are direct loanwords from one language into another, or Wanderwörter, words that spread over long distances via trade.
For the first category, look at sabbatum, the Latin word for the Jewish day of rest. This is quite definitely borrowed from Hebrew שַׁבָּת (shabbāth), since Latin didn't have a good word for "one day out of every seven that's important to the Jews", but Hebrew did.
For the second category, look at the words for "wine": Latin vinum, (very) Ancient Greek ϝοῖνος (woînos), Hittite wiyanas ~ Hebrew יַיִן (yayin), Amharic ወይን (wäyn), etc. Words looking very similar to "wine" appear all over the place, in Indo-European, Semitic, possibly even Kartvelian; it seems likely that some ancient group figured out how to make wine and started trading it, and the word spread along with the concept, ending up with descendants in a whole lot of unrelated language families.
Common roots could mean "any roots that are used in some languages in both families". I believe Draconis has answered that question.
Alternatively, it could mean, "is there a common origin between the Indo-European and Afro-Asiatic families of languages?". The answer to that question is that we do not know. There is no 'compelling evidence', but there are some hypotheses about a Nostratic (super-)family. I believe these hypotheses are somewhat controversial, nor are they entirely discounted as pseudo-science.