Who was the first republican Texan elected to US Senate since 1800?

I am not sure your question is accurate. John Tower was the first Texas Republican senator elected since Reconstruction, but that would mean since 1870-- not 1800. (Since Texas was not admitted to the Union till 1845, it would be impossible for anyone, Democratic or Republican, to have been sent to the US Senate prior to that date.) John Tower was elected in 1961, and resigned in 1985.