If I have a card, does my landlord have to let me grow at my house or apartment?

No.

The property owner has no obligation to permit you to grow on his property. Your recommendation to use Medical Marijuana does not constitute a medical order. Therefore, he can choose to prohibit you from growing there or even from smoking inside your own house, if your lease says that you cannot smoke inside.

The card does not grant you special permission or protection with regard to landlords, leasing, etc.