Easy fix. Step 1: Disconnect negative battery cable from battery!
Step 2: Remove nasty charred wire and say a prayer for whoever/whatever blessed you that your car didn't burn to the ground! You can chant or put a pentagram with candles down, I don't care which.
Step 3: Replace wire, tying it and snugging the nuts down on both the starter and alternator.
Step 4: Reattach battery ground lead.
Step 5: Measure battery voltage, should be in the neighborhood of 12.1 to 12.2. Start car and measure battery voltage, should be in the neighborhood of 13.5 to 13.8.
Step 6: Crack open a barley-pop!
PS: my car came with a #10 from starter to dash. I added an 8 gauge that powers a heater, an audio amp, and a few other accessories like USB ports and Cig lighter.
My advice is replace it with a #8 or #6, as others have mentioned.