Only the President and the Vice president of the clan have privilege to invite other players to the clan.
Steps to invite a player to your clan:
1) Open friends tab on the homescreen.
2) Tap on a player who hasn't joined a clan to open his player profile.
3) Tap on the 'Invite to Clan' button that is displayed on the player's profile(only if the player is not a part of the clan and satisfies the clan requirement criteria)