You can by splitting the string. the [..] operator lets you access object properties by name (and array items index). In a case of nested objects, you simply access them one after the other.
Try like this:
var person = {
name: 'Joe',
contact: {
phone: '555'
}
}
var nameOfPerson = person['name']; //Joe
var str = 'contact.phone';
var phoneToPerson = str.split('.').reduce(function(o, key) {
return o[key];
}, person);
alert(phoneToPerson);