Wire gauge is determined by the crosssectional area of the conductors not the diameter of the cable which can vary more than a little depending on the thickness of the insulation. The other posters are correct any plugs you are likely to buy will accecpt #16, once the insulation is removed.
But don't confuse a concern about thick vs. thin, influence a decision as to the appropriate size to use.
It could be 12 AWG, 14 AWG, 16 AWG, and gasp, even 18 AWG.
Win some bets. For the vast majority of home systems with the speaker wires running within the room, people just won't be able to hear a difference (in blind testing) between any of them. People will say that they can, but never as the result of a good blind test.
Folks will jump in with the Roger Russel site, and it is a good one. But read it carefully, especially the
table on this page before you buy off on 16 AWG as too thin (whatever that means).
For what it may be worth I use in my 13 x 22' room #12 for the mains (because I like the look), and # 16 for the side surrounds. The rear surrounds are on a combination of #16 under the floor and #18 where it is exposed. #12 used to be a bit large for many plugs, but these days marketers have caught on and some screw down plugs are so large that #18 has to be doubled to get a good fit.