Whilst you can add your social media links to your profile as simple links in either the text or in a list of links, you might instead choose to add them under the social media links section. Doing this will display the social media links with the appropriate icon and display the link on all pages of your profile.
Note: some profiles may have social media links disabled, if you do not see this setting when editing your profile then it has been disabled.
To manage your social media links, go to the 'More Options' screen by clicking on the small 'More options' link in the top right of your edit profile screen:

In the 'More options' screen click on 'Social media' link at the bottom of the menu on the left hand side:

Simply paste in the URL to your social media profile in the appropriate textbox:

Note: the list of supported social media platforms may change as others are added in the future.
To remove a social media link just delete the link from the text box.
Once you have made your changes, click the 'Close' button and when you next 'Save changes' to your profile your social media links will be updated.