Chiamami per favore is the Italian translation of the phrase 'please call me'. As an instruction, this would be the most accurate way of translating it, although if you were posing it as a question- as in 'Will you please call me?' you'd have to rearrange the structure of the sentence slightly to something more like Mi chiami per favore? or Mi potresti chiamare?.
Per favore is the Italian word for 'please' (literally: as a favor), and it can be substituted for a number of different expressions. Examples of these are per cortesia and per piacere which are both considered slightly more formal.