The answer to the question in the title can be found in a Texas statute called: HEALTH AND SAFETY CODE – TITLE 10. HEALTH AND SAFETY OF ANIMALS – CHAPTER 822. REGULATION OF ANIMALS – SUBCHAPTER E. DANGEROUS WILD ANIMALS – Sec. 822.101. There is a list in this section which includes the bobcat. This means that provided an individual has the requisite certificate of registration to own or have custody of a bobcat when residing in Texas then it is legal. If you don’t have this certificate which I construe to be a licence then it would be illegal.
You have to apply for it on a pro forma application form which will guide you as to what to put in the form. There may be a fee and there will be stipulations and conditions on how you provide for your bobcat. You will also have to expect a visit from the authorities to make sure that you keep records and that your facilities are adequate for the purpose of keeping a medium-sized wild cat which is potentially a dangerous wild animal which in turn is why there has to be a certificate of registration.
At this point I think it would be better if you are serious about owning a bobcat as a resident of Texas then you should click here which will take you to the relevant section of the above-mentioned statute (law).
The rules are different, as you might expect, for circuses, zoos (accredited member of the Association of Zoos and Aquariums), research facilities, certain authorities and activities such as transporting an injured animal and so on. There’s a long list of exceptions for organisations such as these. But they will be regulated by other laws. However, they need not apply for a certificate of registration in order to own a bobcat legally in Texas.
Please remember, however, that the law changes over time so you have to keep your eye on the ball. It may be wise to telephone the local authority to check what I have said in this article. And of course if you’re thinking about owning and taking care of a bobcat you really do have to know what you’re doing. It’s no good thinking that they look cute and you can keep them as pets in your home. That won’t work, I can almost guarantee it. The bobcat is quite amenable to being domesticated but even in that ostensibly friendly state they are still wild cats with all the associated behavioural traits which they bring into your home or enclosure.