Who is the first bowler to take hat-trick in T-20 international?
Brett Lee is the first bowler to take a hat-trick in T20I matches. He took against Bangladesh at Cape Town in World T20 2007. See the scoreboard.
From the match report:
Another Twenty20 first
After the first Twenty20 century, by Chris Gayle against South Africa, this match brought the first hat-trick in the international version. Brett Lee was the man with the honour as his pace proved too much for the middle order...
Here is the list of the hat-trick in T20I matches.