Use an OTG cable and a card reader. (There are card readers made for cellphones, but an OTG cable is usable for other things as well, and the combination is cheaper than the specialized reader.)
Check this product out https://shopmeenova.appspot.com/st/p/m3r.html#devList it was a Kickstarter backed offering that is fully available for retail and will work with many Android devices, they actually tell you if it will be supported or not and the Galaxy S4 is a YES on that list.