I've got logic app under the same subscription as my azure synapse analytics. There is not an inbuild activity in synapse analytics for logic app.
I have tried to call logic app within private network (using managed private endpoints), but I cannot use managed private endpoints as managed private network is disabled.
Inside the Azure Logic app use following activity as a trigger: When a HTTP request is received
After Logic app is saved, there will be generated HTTP URL, which can be viewed and copied if clicking again on the trigger activity.
Then inside Azure synapse analytics pipeline use Web activity. In the settings of the activity paste HTTP UTL (generated by Logic app) to the URL field: