Submitting websites to search engines is not enough to get traffic.
Banner advertising is the best way to get traffic on your social networking site. Do some link exchange, with relevant sites having high PR.

Forum participations, social bookmarking, directory submissions as well as creating communities in other social networking sites can help to get traffic.

Discuss about it in different SN sites/forums and blogs.

Short term strategy is to spend a lot of money advertising your site while using a stats program to track the incoming traffic and make changes until you get a good conversion rate of sign-ups.

Long-term strategy is stated above of posting on other blogs and forums along with submitting some articles to other sites to build links and reputation. You also will benefit from building lots of content so you have a chance of getting some free search traffic at some point in the future.

Also, not sure where you are in development or if I need to view your site on a mobile device, but when I visited your site by following the link, I found a site with no basic explanation about what it is or what you want me as a visitor to do.

Is your site still in development mode? Either way, your site may benefit from some usability tweeking on the home page. The home page needs to entice the visitor to want to learn more about the site and to stay on the site. It needs to be engaging.

Agree with points made by BobChrist and InsightsDigital, talk up your site on other forums and sites and also make it clear on the site what the purpose is. Also, along with the home page being engaging you need to ensure that the whole site is engaging from a users point of view.