There are two ways of approving or denying a follower request. It is through the web or through the Twitter app.
Users can approve or deny followers’ requests through the web by signing to the users’ Twitter account. Going to their profile, clicking on “Followers” button. After clicking the said button, the users need to choose “PENDING FOLLOWER REQUESTS” to be able to see the people who have sent in requests to follow. Users have to option to accept or deny those requests.
To approve or deny twitter followers’ requests using the Twitter app, users should determine first the operating system. If its an Android, under the ME tab, scroll down until they find the followers’ requests. On the next screen, it will show the option to approve or deny each requests or simply approve all the pending requests. If its on iOs, users need to navigate to the ME tab. If at any case that they have followers’ requests, they’ll see a banner under FOLLOWING and FOLLOWERS counts wherein it says “FOLLOWER REQUEST”. Users just have to simply tap the banner. Once tapped, users will see a list of all the followers’ requests. The checkmark is for the approval of the request and X mark is for denying the request.
Note that a follower request can also be approved on this link mobile.twitter.com.