Predicting missing facts in a knowledge graph (KG) is crucial as modern KGs are far from complete. Due to labor-intensive human labeling, this phenomenon deteriorates when handling knowledge represented in various languages. In this paper, we explore multilingual KG completion, which leverages limited seed alignment as a bridge, to embrace the collective knowledge from multiple languages. However, language alignment used in prior works is still not fully exploited: (1) alignment pairs are treated equally to maximally push parallel entities to be close, which ignores KG capacity inconsistency; (2) seed alignment is scarce and new alignment identification is usually in a noisily unsupervised manner. To tackle these issues, we propose a novel self-supervised adaptive graph alignment (SS-AGA) method. Specifically, SS-AGA fuses all KGs as a whole graph by regarding alignment as a new edge type. As such, information propagation and noise influence across KGs can be adaptively controlled via relation-aware attention weights. Meanwhile, SS-AGA features a new pair generator that dynamically captures potential alignment pairs in a self-supervised paradigm. Extensive experiments on both the public multilingual DBPedia KG and newly-created industrial multilingual E-commerce KG empirically demonstrate the effectiveness of SS-AGA