Question is pretty much in the title. Does IntelliJ have native syntax highlighting for .jinja and .j2 files?
If not is there a plugin?
This plugin: https://plugins.jetbrains.com/plugin/7792-yaml-ansible-support offers some support for jinja files.
To ensure that this plugin is associated with jinja files:
File > Preferences > Editor > File Types Recognized File Types scroll down to YAML/Ansible and select itUnder Registered Patterns click the + icon and enter *.jinja.

With this configuration in place your jinja files will open into this plugin. If they do not, then jinja files must be already associated with one of the other Recognized File Types in which case you'll need to scroll through them to find the culprit and remove *.jinja from its Registered Patterns.
With recent version of Intellij, you don't need any plugin any more.
Recognized Files Types, choose Jinja 2 Template
File Name Patterns add *.j2 for jinja2, and/or *.jinja for jinjaFor Ansible yaml jinja 2 templates:
Recognized Files Types, choose YAML/Ansible
File Name Patterns add *.yaml.j2 and *yml.j2
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