I am a Design Architect. I am looking for design consultancy .Should I advertise on Facebook?

Yes, you can advertise on Facebook but before that you should build good friend group related to your niche which will help to get good design consultancy in the rapid way.

Yes, you can make an ad on Facebook. In these days, social media is growing at rapid rate. Make a friend circle related to your niche and also join groups on Facebook and communities on Google plus.