Although it is often used (just as the incorrect "orientate" is often used), "administer" is the verb form for administration or administrator.
The word administrate is an incorrect form of the verb created by some who drop the -ion suffix of administration.
Incorrect: He did a great job of administrating the estate.
Correct: He did a great job of administering the estate.
Be careful when forming verbs from nouns that end in -ation, as the correct verb form may not end in -ate.