I just did a quick search and it looks like you have to call your county board of elections to get this, unless somebody else can come up with a better answer???
Contact your township or city clerk. Or check if they have a map on their web site. If you're using the lists, you shoul dbe able to figure it out yourself though.
I just went to my local Board of Elections and printed one out for $2.00. That'd be my first call if I were you. They can at least point you in the right direction.
I found my boundaries on my county's web site. I would suggest that you look in a similar place, or call your clerk office on how to find the information.
you need to choose State Senate Districts then choose the County from the drop down list on middle left side of the screen. Then use the map features to move around and look at your precinct. This is time consuming but it works.
In Texas it's usually either the Clerk or the Tax-collector office at the county level...who run the election info including voter file info in each county (at least I think that's the name of the office). Anyway, ask them who has precinct maps.
You can get them for most areas of the country...there also are private vendors.