last commit here is several years old
git://git.eclipse.org/gitroot/jgit/jgit.git
have newer versions like
JGit v4.0.0.201506090130-r
Contained in tags: v4.0.0.201506090130-r
Commit hash: 4f221854556991e3394b3a71e77ee0b771b1500b
Date: 2 weeks ago (09.06.2015 8:29:27)

see also
gitextensions/gitextensions#2516

earlier attempt:
https://github.com/henon/GitSharp

slluis:
"The really hard parts are:

1. Java constructs that make sharpen crash. When sharpen crashes is not always easy to find out what caused the crash.
2. Java constructs not supported by sharpen.
3. Incorrectly generated C# code. It has to be manually patched.
4. Missing implementations of core java methods. Those have to be implemented or mapped to existing .NET methods using the configuration file.

Some of those problems could be alleviated by improving Sharpen, but only to some extent, since there are some Java constructs which are not easily translatable to C# (and JGit uses many of them)."

https://github.com/pvginkel/gitter/issues/15

NGit does not provide a Stage function which would make deleted files be marked as staged deletes.
mono/monodevelop#653

GPL/LGPL questions with Sharpen.Unix
mono/sharpen#39

weak documentation
#13

I think it should be possible to run JGit on mono directly with ikvm, but can't find posts about it.
UPD:
https://github.com/mono/jgit-binary
http://tirania.org/blog/archive/2009/Oct-12.html