My car is registered in California and is due for a smog check.  I am
currently in Texas for work.  If I pass a smog test here in TX, will
the CA DMV accept these results and renew my registration?  If yes,
what kind of things do I need to go through to get this done? Are
there specific places in the Austin, TX area that can take care of
this for me?

Please include detailed research and links to sources.

Unless you're only in Texas for a brief time, you'll need to get Texas
plates for your vehicle:

http://aig.home.texas.net/register.html

"Q: My renewal notice says my car needs a Smog Check. But the car is
out of state, and will not be back for many months. It's too far to
bring it back to California for a smog inspection. Can I get the car
smog checked in another state and send the results here?
 
A: Do not obtain a smog inspection in another state; it will not be
valid here. Unless your vehicle is in Nevada or Mexico, you need not
bring it back to California in order to complete your registration.
Simply fill out and sign DMV's " Statement of Facts " form (you need
the free Adobe Acrobat reader to download and print this form). The
registration tags will be mailed to wherever the car is currently
located."

Source:

http://www.smogcheck.ca.gov/stdpage.asp?Body=/GenInfo/OtherInfo/Frequently_Asked_Questions_Part_1.htm

Link to "Statement of Facts":

http://www.dmv.ca.gov/forms/reg/reg256.pdf

You just have to check a box that says that it's out of state and mail
it in with your registration info.