Can I appeal this for discrimination?

I do not see this as a discriminatory non-hiring. The police almost certainly have very strict rules and your past history is likely in violation of the rules and policies. Nevertheless, if you believe you have documents (that we online cannot view and study) that you believe support your side, certainly take them and your story to a Texas attorney for a complete review.

Good luck.

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In order to make a discrimination claim, you must be able to show that you were treated differently because of being in a particular class protected because of such characteristics as sex, race, age, religion, physical or mental disability or others. There might be an argument that you could make, but there is not sufficient information in your question to make a definite determination. For example, arrest and credit records have been held to constitute impermissible discrimination on a showing that a particular group, for example, Hispanics, is more likely to have a bad record, as compared to non-Hispanics. What you might consider doing is asking the department to give you the specific reason that you were rejected, and it certainly would be worth your consulting an attorney, if you wish to pursue a discrimination claim. Be aware that most attorneys who are experienced enough to provide you with a reliable opinion will charge a fee for an office consultation.