Is it ok to say "call with <person>"
If you want to express that you experienced a phone conversation with somebody, yes, it is correct to say "I had a call with..." in the same way you could say "I had a chat with..." when you don't want to specify how or if you met face to face for a few drinks "I had some drinks with..."
That happens because the construction actually comes from the verb to have meaning experience and not from the noun call. Check the definition #2 here