I was asked to respond to another thread about checking the PGP signature on Android, but a lot has been said here so far, so I'll just add my opinion.
Unfortunately, I don't think there is a secure way of verifying PGP signatures on an Android.
I checked the
OpenPGP site for Android apps, and only found email encryption clients.
A quick glance at the
GnuPG downloads page does list an Android package that was developed by the Guardian Project. If you follow that link you'll be directed to a page indicating the project is no longer supported, and directing you to the OpenKeychain project.
At first glance the OpneKeychain project looks promising; lots of downloads and decent reviews, but the only way I've found to get the software is from google's app store or an alternate app store. It is open-source, so I can download the source code from from github, and build my own .apk after verifying it as safe (assuming I know how to do that.) But I have not found a developer provided, gpg signed .apk binary. Strange.
Then while reading OpneKeychain FAQs something caught my eye; they recommend sharing your secret keys between devices by transferring them via cloud services. Okay, it's an encrypted backup, but come on, what's wrong with a USB cable? Maybe it's just me, I do have trust issues. Including issues trusting app stores for reasons already discussed, and so it should be obvious I'm not alone. The reason we're all here is to keep ourselves as safe and secure as possible. More links added to the chain of trust only contribute to additional risk. So I think I'll stick to side-loading the Electrum .apk after verifying it on a PC with a trusted PGP client.
But don't get me wrong, I'm not always a security Nazi. I've been known to use the google app store to load electrum, but only after verifying the .apk file found the release directory, following the link from the Electrum's downloads page to the google play store. There are obvious risks to this method, but everybody needs to assess their own risks accordingly. I've often said about (hot) mobile wallets that they should never contain more money than your fiat/cash wallet.
I understand that many people don't have PCs these days, and can only access their bitcoin on a phone; to those people I suggest you invest in a hardware wallet that works with your phone. Consider it a very affordable insurance policy.