What is the fuel consumption per mile for a full CEO A320?
For some general numbers, you can look at the fuel economy tables on Wikipedia. They tell you an A320 flying a 1000 NM flight at typical payload will burn 3.13 kg/km (11.1 lb/mi) of fuel. For a 2151 NM flight, it will burn 2.91 kg/km (10.3 lb/mi) of fuel.
As already indicated in the comments, the fuel burn depends on the payload (and to some extend of course the route length). To get more realistic values, you can use the Breguet equation as shown in Peter Kämpf's answer. When plugging in different values for the payload and flight range (all at 3t fuel reserves), you get these fuel burns:

Since you asked about fuel consumption per distance, we can just divide by the trip distance and get this:

These numbers are somewhat smaller than the numbers from the Wikipedia table. The difference is likely caused by additional fuel burn for the takeoff and initial climb.