It's unclear if he'll enter a plea since he doesn't have an attorney.
Authorities say the 58-year-old man abducted his former neighbor from her home near Weatherford on March 1, then drove her to his Corsicana home about 100 miles away. Maxwell was arrested there March 12, and the woman was rescued.
A judge had denied Maxwell's request for a public defender, noting that his net worth is about $200,000.
Maxwell's in Parker County Jail in Weatherford with bond is set at $500,000.