My father had a home equity loan in Texas and has passed away. Can I assume the loan?

It's a possibility, but as others mentioned, there are a lot of variables. Here's what I would want to know before answering your question:

1. When was the date of death? (Have a death certificate ready when you call)
2. Did your father have a will? (If so, be sure to have a copy and confirm where the original is)
3. Was your father married? Is there a surviving spouse living in the house? Is the spouse in agreement? (dates of marriages and divorce would be helpful)
4. How many children (living or dead) has your father had in his lifetime? (you would need, names, addresses, dates of birth/death, and children of deceased children)
5. Where is the house located? Mortgage company? (an old deed would be helpful, as would a mortgage statement)
6. Is the mortgage in arrears?
7. What kind of mortgage is it? Reverse? HELOC?
8. Any other debts or assets of the estate? (make a list: bank accounts, credit cards, etc.)

You will likely need to change the title of the house, and likely need to establish an administration of some form.

This is a complicated quesion without more facts. An assumption of the home equity loan without probating father's estate depends on the lender's policies. You may have to probate your father's will. If you're a beneficiary and are bequeathed the house, or you're the only heir after an heirship/ administration, then you could probably assume the loan. If there are any other heirs or beneficiaries, then an outright assumption is probably out of the question.