California and Texas are both part of the interstate compact system for DMV's sharing information about restrictions on your driving record. It is unlikely for you to get a license in CA if you are under restriction in TX.
Additionally, if you are talking about a job that requries a commercial driver's license, your DUI conviction will make that difficult for a period after your conviction.
These comments should not take the place of consultation with a Texas or California attorney. There are many attorneys in your area who can be found on this website.
Best of luck.
Mr. Buckley is correct in that California, and most if not all states, have an agreement regarding motor vehicle enforcement & intoxication related offenses.
In Texas, DUI means that the person is 21 or under when s/he is stopped (& then arrested) for driving. Texas has a zero tolerance police - meaning they are not prosecuting you for being intoxicated but because you have any alcohol in you that is influencing your ability to drive. DWI means driving while intoxicated and it can be for anyone (although because DUI is a much lesser burden of proof, one doesn't generally see DWI prosecutions on those under 21.)
If you are correct in your question - you got a DUI, it may be that California (or another state) may be more lenient regarding the motor vehicle rules because it is not a DWI. You should get a copy of the judgment & sentence in your case, as well as the disposition of probation, if you got probation - then contact the motor vehicles department in the state of interest and talk with them about the situation.
Moving will not change a conviction. It will be on your record forever and will be enhanceable should you ever be charged with DWI again. Depending on when your conviction occurred, you may be ineligible for a commercial driver's license which means that you will not be employable as a professional truck driver. Of course, if you do not need a CDL to work for the company, then you may be OK. There are many variables and possible outcomes for your question and I would need a lot more detail before being able to successfully advise you on the merits of your move and quest for employment.
I suggest you contact a top notch DWI Lawyer to advise you about this before jumping in because you may not be able to work as a commercial driver since any suspension and convictions will follow you and be reportable to California.
Sign up to receive a 3-part series of useful information and legal advice about DUIs.