There is no dedicated Logstash output plugin for ArangoDB on the Logstash plugins page, so I had already accepted to write one on my own.
Browsing the plugins page for inspiration, I found an HTTP output plugin for Logstash. It seems to be general enough that it can send the log event in JSON format to any HTTP-speaking backend.
ArangoDB’s API is JSON over HTTP, so it sounded like a perfect match. I briefly tried it out and it seemed to work fine.