According to the official Jira documentation...

During evaluation, JIRA will run well on any reasonably fast workstation computer (eg. something purchased within the last two years). Memory requirements depend on how many projects and issues you will store, but 300MB – 1GB (of Java heap size) is enough for most evaluation purposes.

So, it would be possible to run Jira on a 1GB droplet but I would recommend at least a 2GB to ensure you can allocate enough memory to Java.