Background

I just began working for a religious non-profit organization. As with most non-profits, the organization is resource-poor and has no IT department to speak of. In my two months here I've received 20 requests for websites, apps, and internal automation. Many of these 20 requests have merit and would benefit the organization.

I'm a .net web developer and as such the open source community is relatively foreign to me...

Question

For the sake of this question, lets say I'm talking about building a single, large, website.

Does software (web based, hopefully) exist that would allow me to post requirements and assets (graphics and CSS) for a site, and then invite programmers to participate in the sites development?

As a simple example, I could post the requirements and data for the about us page and an individual would indicate that they could/would fulfill the requirement. Upon completion, they could upload the new source code to the shared repository (github).