The State newspaper reports 58-year-old David B. Conditt was arrested without incident in Charleston on Monday by federal marshals and county deputies.
Police Sgt. Eric Peters of Haltom City, Texas, tells news outlets officers found 58-year-old Dena Wright dead from multiple stab wounds early Thursday. She earlier had taken in Conditt, her twin brother, after he was homeless for a time.
Authorities who arrested Conditt in South Carolina also found Wright's car, which authorities believe was taken after the killing.
A friend of Wright, Keli Stallings, tells the Fort Worth Star-Telegram that the victim talked about her brother having mental problems.
Conditt is jailed awaiting a return to Texas to face charges.