Yes, you can take edX courses using your smartphone or tablet.
The free edX mobile app has Android and iOS versions. The Android app is available in the Google Play Store, and the iOS app is available in the Apple App Store.
Most components of your courses will function in the app or a mobile browser, but some might not, depending on the content of the particular course. At times you might need to use a computer with an up-to-date version of Firefox or Chrome to complete tasks.
For more information about using the edX mobile app, see What can I do on the edX app?