Is a ophiuchus a zodiac?

Ophiuchus is a zodiac in the astronomical definition of a zodiac, i.e the Sun passes through Ophiuchus on its way across the sky.

In the astrological sense though, it is not. The Babylonians decided they only wanted 12 zodiacs, so they left Ophiuchus out. This site has a good explanation of what's up with Ophiuchus: