Apartments For Rent In Alcorn County Ms . The median gross income for households in alcorn county is $36,163 a year, or $3,014 a month. New alcorn county apartments available now. 1 Northtowne Dr, Corinth, MS 4 Bed, 4 Bath SingleFamily Home 21 from www.trulia.com View photos, floor plans, amenities, and more. On point2, the alcorn county, ms homes for rent of your choice are just a few clicks away. Fayette county homes for rent (18) limestone county homes for rent (74) desoto county homes for rent (165) gibson county homes for rent (2).