Yes, you can watch Twitch on your TV by casting your screen from a device that supports Twitch onto your Roku TV. Alternatively, you can use a Chromecast device, an HDMI cable, or the screen mirroring feature on your TV to cast Twitch from your PC to your TV. If you have an Apple device and your TV supports AirPlay, you can also AirPlay Twitch to your TV. While Roku doesn't have its own internet browsing app, you can use screen mirroring to surf the internet on your Roku by downloading an internet app like Opera, Poprism, Web Browser X, or Chromecast from the app store.