No. They keys to semi auto size are breechface and magazine. The g23 only fits a 10mm breechface and 40 length mag. You could convert to 9mm, but if Ben that is suspect.
If you like the G23 consider a G29. They are about 1/8 thicker, but almost identical in other dimensions and will take the 15 round G20 magazines. There are also some hotter 40 S&W loads from Double Tap and Buffalo Bore that will match or beat a lot of 10mm loads.
The problem isn't finding a conversion barrel -- the problem with wanting to run 10mm in a Glock 23-sized gun is that the gun's grip size is too small: a 10mm round just won't fit in the 23's grip frame. The overall length of the 10mm round is 1.26", while the .45 GAP (which will fit in a 23-sized frame) has an overall length of just 1.07".
Glock makes a sub-compact 10mm -- the Glock 29 mentioned by jmr40 -- but not a 23-sized Compact in 10mm. The Glock 29 is a bit smaller in most ways than the 23, and has a shorter grip which holds that holds fewer rounds with a flush-fit magazine. Higher cap mags are available.