Can human skin tan through a glass window?
According to this article by http://Skincare.org - Sun Hazards in Your Car - glass filters out the suns UVB rays. However, it unless the glass is specially treated, it does not filter out UVA rays which can still cause skin damage in the forms of photoaging, sunburn, and skin cancer. Therefore yes, you can still get a tan through a glass window.
The best way to protect yourself when you're in the sun is to wear broad protection SPF lotion that protects from both UVB and UVA rays. My current sunscreen of choice is this Bioré UV Aqua Rich Watery Essence. It's light and does not leave an oily feeling or white cast. Hope this helps!