Preheat your grill to medium heat.
In a small bowl, mix together the minced garlic, chili powder, cumin, paprika, garlic powder, onion powder, salt, and black pepper.
Rub the spice mixture all over the chicken, including under the skin and inside the cavity.
Open the can of beer and take a few sips to make room for the chicken.
Place the beer can in the middle of a roasting pan.
Carefully lower the chicken onto the beer can, with the can inserted into the cavity.
Move the chicken and can onto the grill, making sure it is stable on the can.
Close the grill and cook for 1 hour and 30 minutes, or until the internal temperature of the chicken reaches 165°F.
Carefully remove the chicken from the grill using tongs and place it on a cutting board.
Let the chicken rest for 10 minutes before removing it from the can and carving it into serving pieces.
Serve with lime wedges for squeezing over the chicken.
Enjoy your Tex-Mex Beer-Can Chicken!