Try entering the mysql environment on the droplet via mysql -u root -p (mysql root password is usually in /root/.mysqlpassword or /root/.digitaloceanpassword).

Then grant privileges to all hosts accessing the database with:

mysql>GRANT ALL PRIVILEGES
ON database.*
TO 'user'@'%'
IDENTIFIED BY 'newpassword';

Then refresh the privileges with:

mysql>FLUSH PRIVILEGES;

Source: Similar Question

Replace user and newpassword with what your node app uses.