Look for the Stereo Out RCA jacks on your mixer. These jacks will be red and white. Color match your RCA cable ends into these two jacks.
Insert the other end of the converter cable into the Audio Input jack on your computer. This jack will be 1/8 inches in width. The location of the jack varies depending upon the computer. Check your Mac's user guide for the location of the input.
Turn on your computer. Click the "Apple" icon in the upper left corner of the Mac desktop. Select "System Preferences" and then choose "Sound." Choose "Sound Input" on the drop-down menu. This changes your Mac's sound card to accept an audio input signal from your mixer.
Open a recording application. Plug your mixer into an electrical outlet and turn it on. Create a new audio track within the program. Make sure your vocal microphone has been connected to the mixer. Click the "Record" button on your application to start recording. Click the "Stop" button on your application to end the recording.