It is targeted at students and had earlier been restricted to invitees at universities and schools in the US.
The service integrates with Facebook and is being pitched as an "experiment" rather than a rival to other networks.
Microsoft revealed that the product was developed by its Fuse Labs unit as a "research project... focused on the future of social experiences and learning."
Members are invited to create "collages of content" using the firm's Bing search engine technology and external links, which they can, then share with others.
Users can then identify people who are interested in the same topics, monitor their associates' feeds and take part in "video parties" during which members watch online videos together, commenting on them via chat function.
Members can sign in using their Facebook login details, however, their So.cl activities do not show up on Facebook's pages unless the option is activated.
The move to open up the service to the general public was taken over the weekend with little fanfare, prompting some analysts to speculate that Microsoft only had limited ambitions for the project.
"The fact that So.cl is targeted at students echoes Facebook's beginnings and has made many assume it is a Facebook clone," the BBC quoted Eden Zoller, principal analyst at technology consultants Ovum, as saying.
"But So.cl is, as Microsoft stresses, an experiment designed to be a layer on existing social networks.
"Microsoft is being sensible in positioning So.cl in this way - the opposite approach of Google, which entered social networking all guns blazing with a full on service, and is having modest success," Zoller said.
Zoller added that the project could also help Microsoft further improve Bing's search capabilities.
A study by Comscore suggested that Microsoft had a 15.4 percent share of the US search market in April compared with Google's 66.5 percent lead.
Earlier surveys have suggested that the gap is even wider in the UK and parts of Europe.