If you're here in the US, yes you can! There are some requirements by the IRS in order to be able to do this though. It's not simply a matter of writing a check to the startup.
The key is rolling over the funds into a corporate retirement account (unless it's already in one). That permits you to invest in a private business.
I would suggest asking a CPA to get the nitty gritty details on how to comply with the IRS regulations on this.