The Open Radio Access Network (O-RAN) is a new, open, adaptive, and intelligent RAN architecture. Motivated by the success of artificial intelligence in other domains, O-RAN strives to leverage machine learning (ML) to automatically and efficiently manage network resources in diverse use cases such as traffic steering, quality of experience prediction, and anomaly detection. Unfortunately, ML-based systems are not free of vulnerabilities; specifically, they suffer from a special type of logical vulnerabilities that stem from the inherent limitations of the learning algorithms. To exploit these vulnerabilities, an adversary can utilize an attack technique referred to as adversarial machine learning (AML). These special type of attacks has already been demonstrated in recent researches. In this paper, we present a systematic AML threat analysis for the O-RAN. We start by reviewing relevant ML use cases and analyzing the different ML workflow deployment scenarios in O-RAN. Then, we define the threat model, identifying potential adversaries, enumerating their adversarial capabilities, and analyzing their main goals. Finally, we explore the various AML threats in the O-RAN and review a large number of attacks that can be performed to materialize these threats and demonstrate an AML attack on a traffic steering model.