If a 960 will fit, then a EVGA 1060 SC will fit. They have the same power consumption and a reference 960 is larger than EVGA 1060 SC. But you really need to get a better power supply. A 960/1060 requires a 400W recommended.
GTX 1060 Specs -
http://www.geforce.com/hardware/10series/geforce-gtx-1060
Recommended power supply upgrade - http://www.newegg.com/Product/Product.aspx?Item=N82E16817151094&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-PCPartPicker,%20LLC-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=