I live within 15 miles of an international airport. Is it possible to rig my radio to hear the control tower contacting planes at this distance or at all?
No but you can buy a radio that you can listen with. Goto Radio shack.
This is a better question for the forums at LiveATC.net. But I’ll answer it here.
For your radio? no. you won’t be able to hear it at all on a normal FM radio unless the airport has something set up for you to do it. You’ll need a scanner, as Civil/Commercial air frequencies start somewhere between 118.000MHz and higher. Normal radio only goes up to 107.9MHz. Even with a scanner, you’ll need to have line of sight with the facility broadcasting on those frequencies. If you don’t, you won’t hear it.
Normal FM radio operates downward, with their transmission tower situated somewhere high, broadcasting down. Air Traffic broadcasts the opposite. Their facility broadcasts upward and outward. So the closer you are to the ground and further away from the facility you are, the less likely you’ll hear any transmissions except from the pilots in the air (which you will always have line of sight with until they fly out of your area).
Have a look at LiveATC.net. If you’re in a good place, you might be able to provide a feed for them there. They’ll have the details on all of that plus more.
BL.
The short answer: no. You’re basically too far away from the airport to hear the tower. You’ll just pick up the pilots’ side of the conversations.
Check out LIVEATC.net and see if there’s a feed available for your airport.
The OP lives near PHL which has been down on LIVEATC for more than two months.
Oh.
I’ll add one more thing here. Whether your local airport supports it or not is a good question (the two near me in Vegas do!). But it could be that the airport authority will broadcast ATC comms over FM radio for the airport on a limited scale. KLAS and KVGT do, but point theirs to a very specific location, low powered, and on a very short range.
KLAS has theirs broadcasting directly towards the parking/settee area adjacent to 25L/R on Sunset Road.
KVGT has theirs pointing towards the parking area and park between the approach end numbers for 12R and 7, at the corner of Decatur and Cheyenne.
Both broadcast the tower Tower frequency (119.9 for KLAS, 125.7 for KVGT) over 101.1MHz.
I don’t know if KPHL does this, so YMMV.
BL.
On my radio if I set the tuner as high at it will go it picks up the local VOR on 109.0. 
Get some specialized equipment as mentioned above.