Yes, it is possible to transfer money abroad with your cell phone. The most secure way to do this is to use an established, reputable company like PayPal. You simply download the PayPal application to your mobile phone (visit https://www.paypal-marketing.co.uk/sendmoney/index.htm to find out how). Once downloaded, all you need to do is log in to your account and enter the amount you would like to send and the recipient's phone number or email address. You can send money in 23 different currencies and directly from your contacts list.

See, What is PayPal?
See, What is the safest way to pay online?