When you package your project (*.aia) in App Inventor, a new *.apk installer will be made than can be used to install your app on Android devices. There doesn't seem to be any other program or service that could handle App Inventor's AIA format.
Convert App Inventor project to Google Android application package.
We have found one software suitable in our database for this conversion.
On-line services software - convert aia to apk on web
A cloud based Android app development tool
Convert from aia file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.