Current State:

Currently, the API supports reading icons, but not writing them.

• [Get icon {id}|https://developer.atlassian.com/cloud/assets/rest/api-group-icon/#api-icon-id-get] - Load a single icon by id
  * [Get icon {id}

  icon.png|https://developer.atlassian.com/cloud/assets/rest/api-group-icon/#api-icon-id-icon-png-get] - Load a single icon PNG by id

• [Get icon global

  https://developer.atlassian.com/cloud/assets/rest/api-group-icon/#api-icon-global-get] - Return all global icons i.e. icons not associated with a particular object schema

Proposed Future State:

Provide a public API for create/upload Icons in Assets.
 

Alternative (e.g. Third Party Plugin):

Use the UI to upload the icons.