As a person with German citizenship and permanent residence abroad, you are not subject to the general registration requirement and therefore not subject to the ID card requirement within Germany.

However, you can apply for an identity card in person at selected German diplomatic missions abroad that have been designated as identity card authorities by the Federal Foreign Office or, under certain conditions, at any citizens' office in Germany.

Please note:
Please enquire beforehand at the diplomatic mission in whose district you are staying whether it can issue identity cards, as not all diplomatic missions abroad are also identity card authorities.