Q: Can I record the audio from a cassette player (portable) into my Mac Mini 2012?

The mic inputs on the on the Mini only support mono.

For stereo input you need an USB audio adopter

http://www.sweetwater.com/store/detail/UCA222?adpos=1o1&creative=55225946401&dev ice=c&matchtype=&network=g&gclid=Cj0KEQj…

I think you mean adapter not adopter.

I have several old cassette tapes that I'd like to digitize.  Can I do that by playing the tapes on a portable cassette player plugged into the audio in port on the back of my 2012 Mac Mini?  If I can, what plug do I need,  a simple stereo (ground, left, right) mini plug?  Do I need a pre-amp?

Yes, the audio input on your MacMini is stereo and line level. (It is not a Mic input.) You need a stereo miniature phono plug (3.5 mm) on the end that goes into the MacMini. You do not need a pre-amp.

As far as software goes, you can try 3rd party software, like: http://audacity.sourceforge.net

or

Just use Quicktime:

The mic inputs on the on the Mini only support mono.

The seperate audio inputs on a MacMini are not Mic inputs, they are stereo line level audio inputs.