Yes, you are eligible for MBA course.

You can write entrance exams like CAT, MAT, XAT and SNAP. You need to first clear the written exams and then comes the stage of Group Discussion and Personal Interview.

CAT is the main entrance exam for MBA. The eligibility criteria of the Common Admission Test or CAT refers that any MBA aspirant who has completed or appeared in the Bachelors Degree final examination with minimum 50 per cent aggregate are eligible to appear for the test. For the reserved category candidates, such as Scheduled Caste (SC), Scheduled Tribe (ST) and Persons with Disability (PWD), the minimum percentage to be secured in Bachelors Degree is 45 per cent.

To check the complete eligibility criteria you can refer below link

CAT Eligibility Criteria

If you are interested you can go for HR Specialization because you are political science student you have skills in regard of  good relationship with the people.

All the Best!!