No, you will not normally be able to get a driver's license in California if your license is suspended in Texas. All states are "sister" states with Texas so you will have the same issue in other states as well if you apply for a license with a suspension on your TX license.
The California Department of Motor Vehicles (DMV) says that in order for one to get a driver's license here they must verify through the acknowledged national driver record data source that there are no stops, holds, or other impediments to the applicant obtaining a driver's license in California.
The national database the CA DMV is referring to is the National Driver Registry (NDR) which all states enter information into about problem drivers. It is a federal mandate that all states check this when a person applies for a driver's license or goes to renew a driver's license.
If you show up as a problem driver on the NDR you cannot usually obtain a license in any state. Problem drivers according to the NHTSA (the administrator of the NDR) are those with DUI convictions on their record, suspended license, revoked license, canceled license or other licensing issues of this nature.
When applying for a driver's license in California or any other state their licensing agency will check the NDR and see that your suspended license in Texas. Your application for a driver's license will then be denied in CA or another state until you take care of your license issues in TX which means getting the suspension ended and your license reinstated.
Not having a valid license will make it difficult when moving to a new state if you plan on registering a car since car insurance companies require a valid license for your car insurance policy. If you cannot obtain a valid license but want to register a car, or re-register one in Texas, then you will need to shop around for an automobile insurance company that will allow you to exclude yourself as a driver and put the person that will be driving you around in your car as the primary driver. Their driving record will be looked at instead of yours.
With CarInsurance.com you can find the auto insurance for your needs. Due to your license suspension your car insurance rates are bound to be higher so come to CarInsurance.com and let us help you check car insurance prices.