Archibald Alexander was one of the pioneers of Union Township entering 160 acres in Section 28 and 80 acres in Section 33 in 1833, 80 acres in Section 33 in 1838 and 80 acres in Section 20 in 1848. In 1837, Gilbert Harney organized the Lizton Christian Church in the Alexander home. The 1885 Hendricks County history lists him as settling in Union Township before 1835. In the same reference, he is listed as the Justice of the Peace for Middle Township in 1835 (which then included Union Township). The 1914 Hendricks County history lists him as serving in the Indiana Senate from 1842 to 1845.
He married Sarah/Sally Bledsoe in Mason County, Kentucky on March 6, 1815. They were the parents of a son, James P., and a daughter, Elizabeth.