Preheat the oven to 350°F (175°C).

In a large mixing bowl, use an electric mixer to beat the cream cheese and sugar together until the mixture is light and fluffy. Add the eggs one at a time, beating well after each addition. Mix in the sour cream and vanilla extract until the batter is smooth and fully combined.

Scoop out one cup of the cream cheese batter and place it in a separate small bowl. Stir in the orange extract along with the yellow and red food coloring until the mixture is evenly tinted a bright orange.

Pour the uncolored batter into the prepared 9-inch graham cracker crust. Drop spoonfuls of the orange-colored batter over the top and gently swirl with a knife to create a marbled design.

Place the cheesecake in the preheated oven and bake for 30 to 35 minutes, or until the edges are set and the center is slightly jiggly. Allow the cheesecake to cool at room temperature for 1 hour. Once cooled, cover it with plastic wrap and refrigerate for at least 8 hours or overnight before serving.