just use the 'https://api.vapi.ai/call endpoint with something like

{
  "phoneNumber": {
    "twilioAccountSid": "sid-here",
    "twilioAuthToken": "authtoken",
    "twilioPhoneNumber": "+1thenumberPlacingCall"
  },
  "assistantId": "assistantIdHere",
  "customer": {
    "numberE164CheckEnabled": true,
    "number": "+1theNumberToCall"
  }
}