I also don't currently have a link to sign in, but that is what I was planning to do.
For reference, here is a preview of what we are close to launching. It is a Wordpress template, so the content is not what we will really have.
http://bizen.csclientsite.com/
old site: http://bizen.com
Your call to action is very clear, "Try it Free" (I'm assuming you're going to make it so that the content on the left of the slideshow/carousel doesn't fade in and out). I think this is a Good Thing (tm).
It seems clear that your goal is to convert new users who land on your home page. I'm guessing the decision between login form versus link has to do with a compromise between conversions and engagement.
That said, without a way for an existing user to find their way back in your engagement is going to suffer dramatically - unless going to your homepage is not the primary way your users access the app. So you obviously need at least a link to sign in.
Deciding whether or not to include a form over a link depends entirely on how much you want to push for engagement over conversion. Your homepage is pretty clean (not a lot of noise), so perhaps there's room for a login form eventually - but since I assume your initial goal is conversions then I'd start with the link.
You can optimize for engagement by making "remember me" the default for logins and then taking logged in users directly to their dashboard when they hit the homepage.
For non-cookied users you could also A/B test the homepage with a link or with a form and then see if you are getting drop off in either conversions or engagement from having one or the other.