The question you should be asking is, why do you want Facebook fans? Is it to retarget visitors to your site through Facebook ads? In that case, a Like button

The question you should be asking is, why do you want Facebook fans? Is it to retarget visitors to your site through Facebook ads? In that case, a Like button on your site would work well. Is it because your app has a viral element that requires appearance on profiles/News Feed to grow? Then you should be incentivizing users to friend you by offering them something of high perceived value in return. Or do you simply want a high number of fans as a growth metric to show off? For that, there are numerous enterprises online that will sell you as many fans as you want at a reasonable price.