I am looking for some program on which I can post an assignment I completed with a rubric, and random people can essentially peer-review and grade it for me and I am able to peer-review and grade other people's work on the website.
How about Moodle?
Moodle is a free and open-source learning management system written in PHP and distributed under the GNU General Public License.
and it's supports peer review assignments too.
The Peer Review Assignment Type allows students to submit documents then review the work of other students. It can be used in classes of 5 or more (usually large classes) and can be used to streamline a series of assignments in a course. It manages the relationships between students without teacher intervention, but with teacher oversight through moderation.