CRM with automatic call logging without PBX

Is there a CRM that allows automatically logging calls from the smartphone?

Basically link all incoming and outgoing call logs for the contacts in your CRM.

We are a very small business, and do not need any other functionality like email marketing, pbx etc (don't have budget for PBX as calling is currently unlimited at $20/month).

Just this feature with a very basic CRM. Budget is $30/user/month.