Yes each and every graduate can apply for joining in CID and CBI after clear in civil service examination.

The Criminal Investigation Department is a crime detection agency under the Government of India. It was established on the 1st of April 1906.

For this civil service examination candidates should require some basic criteria:

Educational:

Candidate should have minimum graduation degree with any discipline from a recognized university.

Age:
General category candidate: 21 to 27 years
OBC category candidate’s: 21 to 30 years
SC/ST category candidates: 21 to 35 years.

Number Of Attempts:

Candidates have only 4 attempts for General category candidates
And 7 attempts for OBC category candidates
Unlimited attempts for Sc/St category candidates