Personal pronouns like proper nouns follow the same inflection rules, as is nicely summarized in a table here: canoonet: Personal Pronouns
The polite form in adressing people actually is the 3rd person form capitalized. The same inflection rules apply.
Now we have to learn by heart which grammatical case goes with any verb. There are no generally valid rules for this. For anrufen it would be the accusative:
Ich rufe Sie (accustive) an.
The example you gave with anrufen is a nice example of inconsistent rules. The correct grammatical case is accusative case but you will also hear the dative in southern regions of Germany and in Switzerland (wrong: "Ich rufe Ihnen an").
With a verb taking another grammatical case (e.g. zustimmen taking the dative) you'd say:
Ich stimme Ihnen (dative) zu.
Also see the following related questions: