Can you get brown spots on your feet from smoking?

Yes: Melanosis, a darkening of skin from increased melanin production, has been reported in smokers. It is commonly seen more where nicotine has direct contact, like in the mouth and around the mouth, but can occur anywhere. If people stop smoking, they tend to fade away, but they don't always completely clear. See a dermatologist to be sure, especially if the areas have changed- rule out melanoma.