No need.
But you can index both fields to speed up queries.

Every table should have a primary key, preferably an auto-incremented primary key

As far as the paradigm of database design is concerned, I think if these two IDs can form a primary key, there is no need to add another ID.

If there is a many-to-many relationship between user and role:

CREATE TABLE user_role (
    user_id INTEGER NOT NULL,
    role_id INTEGER NOT NULL,
    PRIMARY KEY (user_id, role_id),
    KEY (role_id)
);

In this way, you can not only check all permissions of a certain user, but also check all users with certain permissions (such as super administrator).