A marriage may be annulled if, at the time of the marriage, the person seeking the annulment was under the influence of alcohol or narcotics and did not have the capacity to consent to the marriage. However, it is important to note that, the person seeking the annulment cannot have voluntarily lived with the other person to the marriage since the effects of the alcohol or narcotics ended. So a person regretting a marriage six weeks after the fact cannot claim that he or she was intoxicated and seek an annulment if they have been living together since the marriage.
References: Texas Family Code 6.105
Article by Sarah F. Berry, Attorney