Yes, you can create JIRA issue with WebService IFTTT action (usual IFTTT to create JIRA issues will not work for anonymous users as it does uses the Application link to connect to your JIRA and that will not be available for anonymous users, while web service connection is available to anyone, unless you tell otherwise (setting up connection restrictions))

Here is the demo


{
    "fields": {
       "project":
       { 
          "key": "JTEST"
       },
       "summary": "[entry.summary.escapeJSON]",
       "assignee":{"name":"admin"},
       #set($desc = "[entry.desc2.escapeJSON]")
       #if($desc)
       "description": "[entry.desc1.escapeJSON] \n [entry.desc2.escapeJSON] [entry.mytextarea.escapeJSON]",
       #end
       "issuetype": {
          "name": "Bug"
       }
   }
}