Yes you can join Central Beureau of Investigation unit through combined Graduate Level Examination organized by Staff Selection Commission (SSC)

Eligibility criteria :
To apply for SSC Combined Graduate Preliminary Examination you have to pass a Bachelor's Degree or equivalent of any recognized Indian University.

Age limit :
For Assistant Grade & Sub Inspectors in CBI :: 20 to 27 years.
For Sub Inspectors in Central Police Forces, :: 20 to 25 years.

Physical fitness required for CBI
Chest 76cm
Height 165cm for men
Height 155cm for women

Important dates :
Closing Date for receipt of application: 14.02.2014;
Date of Exam: 27.04.2014 04.05.2014

Now dates for examination are over , next year SSC CGL exam notification will publish in February month of 2015 year

Contact details :
Secretary
Staff Selection Commission
Block - 12, CGO Complex
Lodhi Road,
New Delhi - 110 003, India.