You should be able to achieve that by using the following:

http://<Management_Server_IP>:8080/client/console?cmd=access&vm=<VM_ID>

Lets say the management server IP is 10.20.30.40 and vm id is fdec294c-46c2-46fd-bc0e-fac23bc146b3, then the URL would look like,
http://10.20.30.40:8080/client/console?cmd=access&vm=fdec294c-46c2-46fd-bc0e-fac23bc146b3

Note that you would need an authenticated web session to use the above else you'd see "Access denied. Invalid web session or API key in request".

Please refer to the below API for more details,
http://incubator.apache.org/cloudstack/docs/api/apidocs-4.0.0/root_admin/login.html

-somesh