Taxes for foreign citizen running LLC in Texas
If you will be providing services in the US, then you will need to pay US federal income tax on the net profit from your business. In the US, an LLC can elect how it would like to be taxed for federal purposes, either as a sole proprietorship for one owner or partnership for multiple owners or an LLC can be taxed as either a C or S Corporation. Each form has unique tax and reporting requirements, so you should speak with a tax professional prior to choosing how you would like your entity to be taxed for federal purposes.
Additionally in the US, the individual states can charge taxes and most do in some form or another. The good news is in Texas there is no income tax on individuals or LLC's. Texas does charge a franchise tax on LLC's, Corporations and Limited Partnerships; however, another advantage to having a Texas entity is the franchise tax is zero until you have more than one million dollars in annual revenue. You should also know that a Texas LLC has to file a state franchise return, even if it has no profit and if an LLC is a partnership, C or S corporation, it has to also file a federal tax return, even it it has no income or profit.
If you will be providing all of your services from outside the US, then you will probably need the help of a tax professional to determine if any of the business income is what is known as Effectively Connected Income, which is still taxable in the US or if this is all foreign income which is likely not taxable in the US.