There isn't a GTX 940 model that I'm aware of, so I assume you meant to type 950. If that is the case, then yes, your motherboard can support the GTX 950. GA-970A-D3 has the required PCIe x16 lane, and space for a two slot card.
Although the motherboard has a PCIe 2.0 lane, the PCIe 3 video card is backwards compatible with PCIe 2 and won't suffer any noticible performance loss from being plugged into a PCIe 2 lane.
Specific info on PCIe lane performance if you're interested:
http://www.enthusiastpc.net/articles/00003/3.aspx