RStudio provides a free version on their Shiny Server for all to use. One of the drawbacks of the free version is that it will be public facing and you will not have a login. If you want to use Shiny Server to host sensitive data you will likely want to purchase the license to help protect your data.
Getting a Shiny app hosted is easy, all you need to do is move your Shiny files to the following directory:
/srv/shiny-server/
Once it’s there you will be able to share your apps with anyone with the following URL http://<hostname>:3838/APP_NAME/.