You can turn off promoted tweets via Twitter Settings

Promoted Tweets and Promoted Content are tweets which pop up from time to time to Twitter users based on a combination of their web browsing and Twitter’s ad partners, not necessarily any account you are following.

If you prefer to not see them, you can opt to turn it off through your settings.

This is how:
  1. Login to your Twitter account
  2. Go to Settings
  3. Click on  'Security and Privacy' and scroll down
  4. Uncheck the Personalization and Promoted Content buttons
  5. Click on 'Save' to keep the changes you made

That's all there is to it.