All moral arguments for the existence of God work on the principle that we all have a shared sense of morality. Despite cultural differences, broadly speaking, humans worldwide have a vague idea of what is right and what is wrong; a moral argument for the existence of God would say that this mutual understanding is proof of God's existence.
Immanuel Kant put forward this argument (although, not a moral argument); God as the source of objective morality. Firstly, he addressed the categorical imperative; our own sense of duty, and that being moral was case of following this principle, for example, paying your debts. He said that it was our duty to promote the highest good (summum bonum), however virtue and happiness are independent of one another, in that it is often the case that the virtuous are unhappy and the wicked are happy. Kant then went on to say that it is only in the next life, after death that the union of virtue and happiness must occur (here solving the problem of evil). And therefore, it is logical to presume that there is an afterlife, and consequently a God for morality to exist.
Kant believed it impossible to argue from the world to God (hence why he rejected moral arguments for the existence of God) as he regarded such an exercise to be impossible. However, he did think that God was a postulate of practical reason. The word postulate meaning an assumption of truth as the basis of an argument or theory, although Kant used the term in a stronger sense, to denote the idea of something which is required to be the case. The postulates of morality, for example, denote the assumptions that must be made by anyone who accepts an objective morality. Kant had great trust in the universe being fair, and that if summum bon ...