There is a Qtum Wallet app available on Google Play for Android devices. However, qtum.org does not mention this wallet so I cannot say if it can be trusted. Do anyone here know better if the wallet can be trusted or not?
To move tums from an exchange, personally I installed qtumd, a command line Qtum client by following these instructions (link). Of course a command line client does not have the niceties of a graphical wallet app.