A marginal one at best. Depending on who you ask, some hold that there is some validity to astrology, that the heavenly bodies do have some influence on events here on Earth. Some even tie the twelve constellations to the twelve tribes.
An interesting side note illustrating the existence of astrology in Jewish thought, when Jews congratulate other Jews, they say "mazel tov". Usually this is translated literally as "good luck" - good luck in the sense of "I am happy to hear of your good luck," not in the sense of wishing someone good luck (I once read a Tom Clancy novel where he has the Israelis wishing each other "mazel tov" before a difficult undertaking, which is stupid, and the reading equivalent of nails on a blackboard). Aaanyway, "mazel tov" literally means a "good constellation". So there you have the idea of constellation = fortune.
Judaism teaches that Jews are capable of negating the influences of the stars and planets by keeping G-d's Torah. Basically, our sages teach that G-d has angels assigned to watch over the nations of the world, but He looks over the Jews personally, so to speak. Its similar with the heavenly bodies. The stars and planets play some role in forming the character of an individual, but the Jew (and anyone who wishes can become a Jew) is capable of counteracting that influence with Torah, which trumps everything else.
So, what significance does the Zodiac have vis-a-vis my relationship with G-d? Virtually none.
With G-d's help, I get to decide who I am - not the stars.
I hope you find this information helpful.