In order for any sovereign nation to become a part of another nation, a Treaty of Annexation must be ratified, approved, and adopted. There was a House Joint Resolution inviting US troops into Texas together with a Treaty of Annexation, that was negotiated between the United States of America and the republic of Texas, but the US Senate never did approve and adopt it, but shelved it instead, (like many state enabling Acts), probably because there is no authority in the US Constitution for them to bring a sovereign nation into the United States. Now, after over 150 years, the republic of Texas has withdrawn from their part of the Treaty and a house Joint Resolution has been issued ordering US troops out of Texas.

For more history about the republic of Texas see here