There is no archaeological evidence of the Exodus. When you get down to it, it's surprising how little archaeological proof there is of many things which we're pretty sure happened - we have difficulty identifying some entire nations which are described by sober ancient historians; and there are many monarchs who are known only by a single reference in a stele or inscription that we happened to dig up. In any event, there's no archaeological evidence for the Exodus.
What's more of a problem is that we don't have evidence for a massive change in the population of what-was-Canaan around the time that the Torah describes the Benei Yisroel moving in. Once again, there's not a huge amount of evidence one way or another; partially because our ancestors failed to create massive archives of clay tablets, partially because they kept living in the same area and building over (or reusing) the remains of older buildings. None the less, the archaeological record doesn't support the Jewish narrative.
For what it's worth, I think that any attempt to "prove" the Torah via archaeology is doomed to failure. Even if a substantial bit of evidence supporting the Exodus were found - say, finding the altars and pillars near Mt Sinai - the entire Biblical narrative is so unlikely from a rationalist perspective that almost any explanation (e.g.., ruins of a previously-unknown civilization, a pious Herodian reconstruction, the foundations of a secret IDF military camp) would be preferred.