I'm a freelance software developer too and I pretty much get all my work through LinkedIn. The thing is, my connections are a lot of (pre selected) recruiters. I know a lot of freelancers hate recruiters, but I don't get that. Recruiters often have a foot in companies, you yourself just can't get in. Going through an intermediate also takes away a lot of risks for you and the company... Like if a company goes belly up, you still get paid. The other way around, it saves you making contracts and of course "cold" calling/mailing people for a possible contract, what is often seen as spam.
Just make sure you have all your skills listed and a good description.
I don't care they take a percentage, as long as I get what I want out of it, it's a win win... also when you stay in good contact, it are the recruiters who will probably help you get a contract, when times are less good for freelancers.