Unfortunately, the system administration permission it's required to perform CSV imports on JIRA.
As an option, you can create a script template using JIRA REST API, so your users will only need the Browse Project and Create Issue permissions to bulk create the issues using the Script.
Once you create the template, they will only need to populate the fields with the data of the new issues and run it on JIRA.
Here's the documentation on How it works/What is REST API:
And here are some examples of how you can use it to create issues:
The curl commands to create the issues as mentioned on the documentation can be executed on your machine terminal.
If you have further questions, please let me know.
you don't need to type script or any Rest Api for importing issues or even their links as well.
Firstly importing issue as non admin:
1-On the top menu click on "Issues"
2-Pick up "Import Issues form CSV"
3-Map your file
Secondly in order to import links, your admin have to add "Linked Issue" field on your Create Screen, to aim to see link types. As shown in the image below with mouse cursor.
Ultimately you may specify your outward link, as shown in the image below.
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