Well, you have to have some sort of Internet access to reach those sites. Is cable your only option? Only you can answer that. There certainly are other choices, depending on your location. Cellular, satellite, DSL and fiber are just some options. But not all might be available in your location.
Now if you're asking if the Roku has the ability to connect directly to the Internet by itself, then no. I can only connect to a network that already has access. It can be via wireless, or wired with the correct USB connector. But whatever it connects to must have its own Internet connection.
Roku Stick (2016), 4 and Ultra, Insignia Roku TV, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network. Samsung JU7100 4K TV, Yamaha RX-V679, 40+Mbps DSL from CenturyLink