Missing user password with parse REST Api when linking facebook user
You've missed authData field. Here is the example of JSON from Parse documentation:
{ "authData": { "twitter": { "id": "12345678", "screen_name": "ParseIt", "consumer_key": "SaMpLeId3X7eLjjLgWEw", "consumer_secret": "SaMpLew55QbMR0vTdtOACfPXa5UdO2THX1JrxZ9s3c", "auth_token": "12345678-SaMpLeTuo3m2avZxh5cjJmIrAfx4ZYyamdofM7IjU", "auth_token_secret": "SaMpLeEb13SpRzQ4DAIzutEkCE2LBIm2ZQDsP3WUU" } }}