Yes, you can file RTI Application to know about the Status of your Passport Application.
Matters related to passports come under Consular, Passport and Visa (CPV) Division of Ministry of External Affairs. Passport Authority (Regional Passport Offices) are a "Public Authority" as per Section 2 (h) of the RTI Act.
You can file RTI to the concerned Regional Passport Office either Online or by Registered Post and making a payment of the prescribed fee asking them for recorded reasons to delay in issuance of your Passport.
To know more about the procedure to file RTI Applications Online for Central Government Departments, please refer https://onlinerti.com/how-to-file-rti-online-for-center