Gerrit is specifically designed for this. As described here:
Gerrit is a free, web-based team code collaboration tool. Software
developers in a team can review each other's modifications on their
source code using a Web browser and approve or reject those changes.
It integrates closely with Git, a distributed version control system.
I highly recommend you take a look at this and this for detailed information on integrating Gerrit. For an in-depth workflow utilizing Gerrit, check here.
As mentioned above, to make your life easier, I would definitely utilize the Gerrit Trigger plugin.
This plugin integrates Jenkins to Gerrit code review for triggering builds when a "patch set" is created.
EDIT:
For a code review tool that integrates with SVN, I would recommend Crucible by Atlassian. It is not free, but for small teams it has a one time cost of $10 which is very reasonable in my opinion.
Additionally, there are ways you can trigger Jenkins actions (ie: kicking off a build) based on Crucible events (ie: code reviewed successfully with no issues listed by reviewer). Try this link for more detail on this.
The only downside with Crucible I have issues with is the storage of SVN credentials in plaintext. Atlassian stated here that they are not willing to fix this, and instead encourage teams to use a 'system account' with read-only access. This can be a problem for dev teams that do not have a system account (like mine). Besides that, it is an excellent tool.
