The Astrological rulership of crystals and stones is a real mess. Assigning rulerships to signs is a 'recent' development, being something that was quite rare before the last century. A more traditional view is to assign rulership to planets - 'rulership' here being affinity, that is stones and crystals have some characteristics of a particular planet. Indeed some stones may have the characteristics of more than one planet, and so even traditional astrologers could not fully agree.
As Nevada points out there is much more to Astrology than Sun Signs, so I'll make some suggestions for the way in which you MIGHT go about your quest. I think the final choice must be one that you FEEL is right for you, not just because there's some Astrological correspondence involved. These suggestions are by no means all inclusive, so you might very well develop one or more of them or even find something different that attracts you.
Method 1.
Identify your three key signs, and therefore the sign rulers. Key signs are Ascendant, Moon Sign and Sun Sign. You know your Sun Sign. It's ruler is Mars, so you would be looking there for a stone ruled by Mars. However, you might feel for your purposes the Moon is more important and so you could use your Moon ruler. For the Ascendant and Moon Sign you will need to make use of an online Chart facility such as
http://www.astro.com/
Look for the planetary rulers of the Ascendant and Moon and then look for stones that they rule.
Method 2
This requires a little more information but you might take the planetary ruler of your hour of birth. This is not easy unless you have appropriate software but the starting point is quite easy. If you were born after Sunrise, you could use the planetary ruler for the day - e.g. For Friday use Venus. If you were born before Sunrise, then take the planetary ruler for the previous day - using the same example if you were born before sunrise on a Friday you could take the planetary ruler for Thursday - Jupiter. If you have access to the necessary software you could fine tune this to the hour ruler, or simply post here and I or others can tell you.
Method 3.
Look for the planetary ruler of your chart. Now there's no unique method for finding this but in a sense that doesn't matter, what you are looking for is a planet and stone that works for you. Again we can perhaps suggest strong possibilities here.
Method 4
This requires even more knowledge, but again I can give you an answer - work out your temperament and choose a stone that reflects this.
Now those 4 methods are by no means exclusive but the purpose is to get you to think of what aspect of 'YOU' do you want the stones to be attuned to.
These methods may not work well if you are a 'New Age' disciple, as they do not allow for 'modern' planetary rulers, Uranus, Neptune and Pluto and they don't allow for the translation of rulerships from planets to signs - though if you look closely you will find that the planetary rulerships are still there. Also the planetary rulerships reflect the knowledge of stones in the classical and medieval world. Stones and crystals of more modern usage will not be in the lists. That's not a problem if your intention is to be traditional. It is a problem if you are trying to be 'New Age'.
Remember the final choice must be yours, from stones that you feel an affinity with but if you want to reflect the Astrological 'you' then the above methods might well help. They will also give you food for thought and perhaps the 'quest' may help you 'crystalise' your needs.
As I hope you will realise there is NO right answer in an objective sense, not least because there are only seven traditional planetary rulers (and only10 if you take modern rulerships), so each planet must rule several stones and crystals; but there IS a right answer for you in terms of the affinity you feel.