Both are okay, but I have read somewhere that there is a subtle difference.
In cases like this, using entry to focuses on the fact that you end up in something. On the other hand, entry into focuses on the process of entering. It refers to the general meaning of into.
Check out the examples:
My entry to America is the best thing happened in my life --the focus is on the fact that I entered and ended up in America. The American embassy has rules that define someone's entry to America.
The entry into midtown Manhattan (from Weehawken, NJ) is exciting: the focus is on the process of entering. Lincoln Tunnel is amazing!
Now your case,
As I said, both are okay. But IMO, into focuses more on the entrance and thus entry into is what I'd prefer.
It's worth noting that "in" and "into" cannot always be interchanged:
My father is *into in the Indian Air Force
And I walked right in into the room and it was all camera and eyes on me.