This isn't rsync, but you can integrate a-Shell[0] with iOS Shortcuts. You would need to make the syncing happen in the script instead of in the background though. I use a Python script to create aliases for my email this way, so I don't have to turn on wildcard addressing to my inbox.
I tried to do something similar on my iPhone, but couldn't get a reliable (or any) way to get an rsync script running.
I ended up with pen and paper though, which is best for me all things considered.