Mojo Helpdesk has a form widget you can place on your website. Manage> All Settings> Form Widget
If you want to use the helpdesk ticket form we recommend using a link to the helpdesk portal or use an IFRAME and have the helpdesk form display in it. As an alternative you can copy the form (the HTML) and paste it in your web page. This solution is a great one but the HTML will need to be updated if you use or change custom ticket fields (since the form fields change). Remember that you'll need to enable 'guest requests' in your helpdesk settings to allow unregistered users to submit tickets.