Create a new pipeline that includes a Copy Data activity. The source for this activity will be the output of your Logic Apps query, and the sink will be your Cosmos DB.
Then define parameters in your ADF pipeline if you need to pass any specific data from Logic Apps, like the result of the Run query and list results step.
Go back to to your Logic App, after the Run query and list results step, use the Create a pipeline run action to invoke the ADF pipeline you created. You'll need to provide the name of the ADF pipeline and any parameters it expects.
Please test and tell us :)