Yes, intoxication with cannabis can induce anxiety symptoms (American Psychiatric Association, 2013). Active intoxication with cannabis can induce steady generalized anxiety and worry, and may be difficult to distinguish from generalized anxiety disorder (GAD). On the other hand, intoxication with cannabis can induce a severe panic attack, and may be difficult to distinguish from panic disorder.
Long term use of cannabis can result in cognitive problems. Executive functioning (the part of the brain which plans, filters, and initiates tasks) may become impaired, and as a result, goal-oriented activity becomes markedly reduced. This reduction in goal-oriented activities has also been labeled as amotivational syndrome, which also mimics symptoms of depression. These problems with executive functioning may lead to other problems in job and school performance. Relationships may also become impaired, as there may be less social activities, as the person who has long-term use of cannabis may tend to isolate themselves. These stressors with job/school performance and relationship problems can further exacerbate and maintain anxiety and depressive symptoms caused by the active use of cannabis. And the avoidant behaviors seen in the social withdrawal also can lead to worsening anxiety and depressive symptoms. This may lead to a situation where you have a full-blown anxiety disorder and/or depressive disorder secondary to cannabis use. If you discontinue your use of cannabis, then you may see less anxiety and depressive symptoms within 3 to 4 weeks of abstinence.
There are cannabis users who do not experience significant anxiety symptoms or cognitive problems, and continue to function normally at work (or school) and can maintain their relationships. They may occasionally experience anxiety symptoms when intoxicated, but the anxiety goes away when the cannabis use stops, and the anxiety does not otherwise affect their functioning. However, if you do get anxiety symptoms such as worry, nervousness, or panic attacks while using cannabis, this may be a tell-tale sign that you may develop more anxiety in the future if you continue using. The good news is that if you abstain from cannabis, you may be able to prevent the transformation of the anxiety symptoms into a full-blown anxiety disorder.
For more information on anxiety and cannabis, read my book on anxiety, Anxiety Protocol.