The Roku app will only work controlling a Roku device if both the Roku and the device with the app are connected to the same private network. If your Roku TV isn't on the network, the app will never work. And unless you can connect your TV to a wired network, there's no way to connect it to a WiFi network without a remote.
You can get a generic IR remote that works with a Roku TV for very low cost. Most are under $10-15. Just make sure that they list support for a Roku TV on their documentation.
Dan
Roku Community Streaming Expert
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