Can we associate an asset to a ticket using APIs?

You can use the following curl command : 

curl -u (credentials) -H "Content-Type:application/json"-d' {"helpdesk_ticket": {}, “associate_ci”: {"serial_no'":'99RSH32","name":"SALES-SERV","user": "tom@outerspace.com"}}' -X PUT https://domain.freshservice.com/helpdesk/tickets/123.json

For further information, please refer to the documentation here: https://api.freshservice.com/#associate_a_ci_to_a_ticket