Try an SQL statement like this:
ALTER TABLE 'databasename'.'tablename' ADD 'NewColumn' VARCHAR(100) NOT NULL;
Where 'databasename' is the name of your database and 'tablename' is the name of your table.
or if you want to add it in a specific order (after a particular column in your table) use:
ALTER TABLE 'databasename'.'tablename' ADD 'NewColumn' VARCHAR(100) NOT NULL AFTER 'ExistingColumnName';
OR if you want it to be the first column in the table use:
ALTER TABLE 'databasename'.'tablename' ADD 'NewColumn' VARCHAR(100) NOT NULL FIRST;
(note that if you are already connected to the MySQL DB through PHP the 'databasename' part of the 'databasename'.'tablename' pair is not required)
Hope this helps