States are responsible for laws governing their own elections. The national government places some limits on state discretion (like in the Voting Rights Act) and the Supreme Court weighs in on certain issues when salient (like the controversy over Voter ID) but mostly leaves them alone.
Texas' elections are over seen by the Elections Division of the Texas Secretary of State's office, and detailed in periodic updates to the Texas Election Laws. The nature of these laws, of course, are determined by the Texas Legislature.
Capitol Annex reports on the introduction of a bill that would make it easier for independent candidates to get on the ballot:
Under current law, independent candidates for public office in Texas are required to gather signatures to accompany their petitions to gain ballot access. The number of signatures varies. It is one percent of the total vote received by all candidates for governor in the most recent gubernatorial election for a statewide office, and the lesser of 500 or five percent of the total vote for all candidates for governor in the general election within the confines of the district, (with exceptions in districts with low voter turnout) or 500 for district, county, or precinct positions.
Ortiz’s bill would reduce the number to 500 signatures for a statewide office, and the lesser of 100 or two percent of the total gubernatorial vote within the district for district, county, or precinct positions. To give one some idea of how much difference there is between the current standards and those proposed by Ortiz’s bill, independent candidates Carole Keeton Strayhorn and Kinky Friedman were each required to gather a minimum of 45,540 signatures to gain ballot access as independents in the 2006 gubernatorial election. Both Strayhorn and Friedman each turned in hundreds of thousands of signatures, with each having well more than 100,000 signatures on their petitions declared valid.
