People who travel to Texas are not required by law to quarantine or self-isolate. This is true for travelers who arrive in Texas from other counties. It is also true for travelers who come to Texas from other US states.
In Texas, orders for quarantine and isolation can be issued by local health authorities, the Department of State Health Services, and other government entities. Quarantine and isolation orders can be issued for individual people as well as geographic areas.
There are many overlapping state and local laws that discuss enforcement of quarantine, isolation, "stay at home," and "shelter in place" orders. Below we've collected a small number of laws related to enforcing quarantine or isolation orders that have been declared for geographic areas and individual people or groups. The list is not comprehensive.
Though there is debate concerning the interpretation of the U.S. Constitution, generally speaking, the federal government has the authority to issue quarantines related to interstate activities as well as entry and exit through the nation's borders. See the CDC's page on quarantine law for more information.