In speech, or less formal writing, the older generation still says ring: "Iâ€™ll ring you tomorrow." For the noun, use ring or, rather more formally, call with an adjective "He made a telephone call." It might be easier to use a verbal construction: "She telephoned at noon" or "The President spoke with the Prime Minister on the phone."
With the equivalent nouns, the constructions are different: "make a [telephone] call" but "give [someone] a ring". Note that if you want to say the name of the person being contacted, you have to use the verb: "I'll call you."
See also: 'phone, an archaic version of the contraction.