Yes, in fact from Wikipedia's article on "United States presidential elections in Texas", we can see that Texas has elected a Democrat for president twenty-two times since 1876, most recently electing Jimmy Carter in the 1976 election. Republican candidates have only been elected fifteen times.
The highest percentage vote that a Democratic candidate received was in 1932, when FDR achieved 88.06% of the state's vote compared to Herbert Hoover's 11.35%.
Bear in mind that part of the reason for this historical inconsistency, despite the modern Republican party's relatively strong standing in Texas, is that the Republican and Democratic parties have 'switched sides' ideologically throughout their history - see this related question - and the Democratic Party of a century ago is not particularly comparable to the Democratic Party of today.