You can popup your CRM page when Agents are receiving a call in VICIDIAL and pass Lead info using the POST method. if you want to pass custom fields info as well set CF_uses_custom_fields=Y in the URL as well. This setting can be set at the campaign level in the web form field.

Here is a sample on how to pass the parameters including custom fields.
http://www.mycrm.com?CALL_ID=–A–call_id–B–&uniqueid=–A–uniqueid–B–&ACTIVITY_RESULT=–A–dispo–B–&LEAD_ID=–A–lead_id–B–&PHONE_NUMBER=–A–phone_number–B–&ALT_PHONE=–A–alt_phone–B–&USER=–A–user–B–&PASS=–A–pass–B–&SESSION_ID=–A–session_id–B–&SQLDATE=–A–SQLdate–B–&CF_uses_custom_fields=Y&C_ACCOUNT_NO=–A–C_ACCOUNT_NO–B–&C_MIA=–A–C_MIA–B–&C_NET_FINANCING=–A–C_NET_FINANCING–B–&C_TOTAL_OUTSTANDING_BALANCE=–A–C_TOTAL_OUTSTANDING_BALANCE–B–&C_PRODUCT_TYPE=–A–C_PRODUCT_TYPE–B–&ACTIVITY_TYPE=–A–dialed_label–B–&product_type=–A–C_PRODUCT_TYPE–B-

The next step is to set “Get Call Launch” to web-form so that when an agent receives a call CRM page auto popup.