The pronoun their should agree in number with its antecedent (the noun that it refers to) person, but it doesn't. Person is singular; their is plural. You have to change one word or the other.

Correction #1: A person has to rely on his own conscience. (This correction follows the traditional formula of using a singular,
                        masculine pronoun his to refer to a singular noun of indefinite gender.)

Correction #2: People have to rely on their own consciences. (This correction employs nonsexist language by using the plural
                        noun people instead of the singular noun person.)

Check the following resources for useful practice material: 1) Guide to Grammar and Writing, 2) Colleen Hildebrand's UCI Correction Symbols with hyperlinks.

For additional information on pronoun-antecedent agreement or subject-verb agreement see the LARC Electronic Writing Center Grammar Checklist.