Unfortunately, neither the Dodge 3-year/36,000-mile basic warranty nor the 5-year/60,000-mile powertrain warranty will cover your tires. Damage to tires is usually considered general wear and tear rather than a manufacturer’s defect, which is not covered under a Dodge warranty.
You can always add the MOPAR Road Hazard Tire & Wheel Protection Plan. This add-on warranty provides full repair and replacement of tires from curbs, potholes, or other road hazards. You can also choose a plan ranging from two to seven years, just so long as your car is less than 10 years old and has less than 100,000 miles.