Well, outside of the permission settings allowed in the control panel, there isn't any way to grant yourself additional permissions on the database, so you're probably out of luck trying to use the LOAD DATA command directly.
What format is your data file in? If it's a bunch of SQL, you can load the file in from the shell by executing
mysql -h mysql.example.com -uuser -ppassword < data.sql
If the file is some other type of structured file (CSV, tab delimited, etc.), then what you should probably do is write a parser by hand using whatever language you feel most comfortable with and use its database interface to create and execute a bunch of INSERT queries for you.