Though this is for another version of Android, you may want to check out these installation instructions. There are a few extra steps than the typical clicking on an icon in the Play Store (Source - QGIS Blog):
Enable “Allow installation of apps from unknown sources” –
Download the installer .apk (this download should be fixed and
up-to-date) and open it (on most Androids it will download to a
“Downloads” directory, but may be elsewhere; you can just click to
open the file from your file browser and it should start the
Run the installer and select ‘download and install’. 83 MB of data
will get downloaded. Luckily, it is a resumable download – if it
fails, you can start the process off again where you left off.
Confirm that you want to install (standard Android dialogue) – takes
about 2 minutes to finish this stage.
Run QGIS: “Unpacking post-install data” … 10 seconds.
QGIS requires a supporting service, available from the Play store
“This application requires Ministro service. Would you like to install
it?” Confirm and install Ministro II, only 523KB.
Looks like it needs MORE libraries to run! “Qgis needs extra libraries
to run. Do you want to download them now?” Confirm and install the
QtCore libraries – a lot bigger at 31MB.
In addition, here is a list of tested Android devices from the QGIS help site.