Melt butter in a pan over medium-low heat; whisk flour into the melted butter until smooth, about 1 minute. Stir in ketchup, chili powder, and garlic powder until incorporated.
Slowly stir milk into mixture until smooth. Add tomatoes with green chile peppers; whisk in processed cheese food. Bring to a boil, stirring constantly, until cheese is melted, 3 to 4 minutes. Stir in reserved juice from tomatoes if dip is too thick.