As far as I know there are a few apps that allow for them. But then only the ones made with/for those apps. You can find them on the Google Play Store.
When it comes to regular old Shimejis, you can't run those on the phone. This is because they are executable files, which cannot run on Android phones. Even if you had a phone running Windows for phones, it still probably wouldn't work. Also the phone would need to run Java (not javascript, they aren't the same), this also restricts what you can use on the phone.
So, in the end, if you want them, you would have to use ones like those found on the Google Play Store (or similar download form for apps - Although I would be careful no matter where you download from) and they would have to...