my birthdate is January 2002.can i apply for ICAR AIEEA exam in 2021?

You have not mentioned whether you are asking this for ICAR AIEEA Undergraduation or Post graduation examination as both the exams have different age criteria. For ICAR AIEEA UG 2021 examination except Veterinary, the minimum age for a candidate should be 16 years as on August 31 of the year of examination. Now you have completed your 16 years, and if you meet other criteria as well, you can appear for the examination. For Post graduate examination, the minimum age limit is 19 years as on August 31 of the year of examination. Now you'll complete your 19 years in January 2021. So you are also eligible for the ICAR AIEEA PG 2021 examination.