Can my parents claim me as a dependant if I am married?

[Hal_Al]

Yes, under certain circumstances. For details, see a similar question at https://ttlc.intuit.com/questions/2938663-can-i-claim-my-daughter-who-got-married-on-december-19th-2...

[LinaJ2018]

Your parents can still claim you as long as you are not filing a joint return with your spouse.  An exception to the joint return test applies if you and your spouse file a joint return only to claim a refund of income tax withheld or estimated tax paid. 

Additionally, you still need to meet the rule of Qualifying Child, ( first) if doesn't,  check rule of Qualifying Relative.