Yes, your personal and financial information will be perfectly safe and secure.  Casinos use 128-bit Secure Socket Layer (SSL) Digital Encryption to encrype all the data between your Android phone and the casinos servers.  This is the standard required by major financial institutions so it is very secure.

If you still feel uncomfortable about handing over your Credit Card details online, most mobile casinos offer their players the ability to deposit or withdraw funds over the phone.