Whilst looks can vary with charisma, there are core reasons why the two are directly related to each other.
Firstly, appearance can give one self-confidence and enhanced social skills, simply by dint of interaction in social situations. If people are more likely to start a conversation with you, this will tend to boost self-confidence, particularly if those convert into dates etc. Moreover, given that you will have more conversations than a person of identical 'personality score' (difficult to rationalise, but using the 2e S&P separation of charisma subscores) you will necessarily gain more practice in social situations.
Secondly, charisma reflects how one is perceived to other people. It is clear that more attractive people are perceived better, in general, by other people assuming equivalent 'personality scores'. A test showed that babies had an inclination towards beautiful faces: this is not a social construction; some notion of beauty is inherent.
Thirdly, in a reversal, 'personality' can grant 'appearance'. Someone of high self-confidence will tend to be more confident in their appearance, and carry themselves appropriate. If there are two people of identical physical appearance, but widely different self-confidence, the one of lower self-confidence may attract to detract from her innate beauty by slouching, being hunched, lack of facial expressions etc. The more self-confident one will be *perceived* as more attractive in an interpersonal social context.
Whilst Cha = App is a fallacy, there is a link. To reflect that, I use Appearance as 3d6 + Cha mod. Whilst this can create attractive but uninspiring people of 4 Cha and 15 App; or unattractive leaders of 16 Cha and 6 App, the *trend* is positive.