Yes! The BitGym application can be installed and used for free. No payment information is required.
You will need to create a free user account to access the remaining content in the app.
There is at least one free tour per "category" from the left side menu. These free tours are marked by a blue pin, and will not have the lock icon in the corner.
You can exercise for up to 10 minutes in a free tour. There are 18 total tours accessible in free mode.