No, the Arc needs an HDMI ARC or eARC signal. None of the ports on your projector provide the appropriate type of signal. You might consider an external device, such as the HD Fury Arcana, as discussed here.

Your real challenge, however, will be getting the signal from where the projector is to where the speaker needs to be. Sonos doesn’t really make a good solution for projector systems. 

Thanks @Airgetlam. looks like HD Fury Arcana is additional $200 + adds more wire clutter. so I don’t think Arc is worth it for me at this point. 

As much as I love my Sonos, if I used a projector, Sonos would not be the sound solution for me. I keep hoping they’ll come out with some new hardware of some type that would make it work. So far, they haven’t, but hope springs eternal.