It is legal to hunt all game in the state of Texas with semi auto's. The .223 is also a legal caliber to hunt deer with in Texas. You can do it, but as others have said, it is NOT the optimum cartridge for deer hunting. Just so you know, there are manufacturers out there who are producing the AR-15 platform in hunting cartridges for the exact reasons that you're talking about, alot of people like the platform. You CAN purchase AR's in .243, which is a great deer cartridge. You can also purchase what some people refer to as AR-10's, which is a .308 that will also do the job nicely. As others have said, you can kill deer with a .223, but you have to be using the right bullet (not varmint rounds but rounds for thicker skinned animals) and you must place the shot VERY precisely.
I figured that I would include a couple of links to rifles that are better suited to deer hunting built on the AR platform. Please look at other manufacturers beause I'm sure there are others that produce these calibers, this is just something to give you some ideas if you really like the AR platform. Remember that you could also always get a different upper and have 1.5 rifles, where you can switch calibers if you like the .223. Hope this helps and please be humane, if you choose the .223 please don't use some surplus fmj ammo to hunt deer with.
http://www.dpmsinc.com/firearms/firearm.aspx?id=23 <<.243 AR
http://www.dpmsinc.com/firearms/category.aspx?id=8 << .260 AR
http://www.dpmsinc.com/firearms/category.aspx?id=9 << .308 AR
http://www.rockriverarms.com/Catlist.cfm?Category=05 << RRA's .308's, just click the links to view some of the rifles.
Remington is supposed to be coming out with a camo AR that will be designated as the R-15. I have heard rumors that it is supposedly a bushmaster AR that has the Remington logo and some camouflage on it. I'm not sure if it will come in any other calibers besides .223.
http://www.bushmaster.com/catalog_xm15_PCWVMS20FPRED8.asp <<Bushmaster in camo, but I believe it only comes in .223
I have heard that the .243 AR's are actually AR-10's chambered in .243 because of the different bolt face size. AR-10's don't usually have quite the same universal sizes of parts that AR-15's do, so it's something to consider if you wanted to customize it more or build one from different parts from different manufacturers. Alot of people would recommend that if you are going to an AR-10 platform, just go with the .308 because it is such a soft recoiling, heavy bullet shooting, consistent cartridge. If you wanted to go crazy, DPMS also makes a rifle in the .300 SAUM (short action ulta mag) which will definately work for deer, lol, but it has a bit more recoil than the .308. Hope this helps.