Hello student student you can't write ca cpt exam without registration you neet to register yourself at the institute of chartered accountants of India
Check the CA CPT exam form filling procedure below:

Click on the link above or visit the official ICAI website.

Click on the 'Login/Register' tab. Type in your login-id and password, and click on 'Login'.

Click on 'Apply now' to apply for CA CPT June 2019 exam and fill the application form including details of examination, exam centre, etc.

Upload the mandatory documents like passport size photograph and signature.

Preview the filled in CA CPT exam form 2019. In case of any mistakes, click on Back to Form.

Once satisfies with your form, tick mark the I agree declaration box and click on Final submit
You can also click on the link mentioned below for each and every information related to character accounts cpt registration
https://www.google.com/amp/s/finance.careers360.com/articles/ca-cpt-application-form/amp
Feel free to comment if you have any doubt
Good luck