The chromecast icon shows when the app detects a chromecast to be present on the local network. Make sure that’s the case and if it still doesn’t work it usually helps to close down and restart Popcorn Time.
Before proceeding, you should be aware that the use of Popcorn Time and similar services may be illegal. Much of the content of these services is copyrighted material being shared and downloaded without permission from the owners. The use of these services will often result in a violation of copyright depending on what you watch. If you still choose to use the services you do so at your own risk and it is advisable to follow the law.