I have an Azure Web Role with an SSL endpoint configured using a certificate obtained from my companies Active Directory Certificate Authority, and an Azure Web App that nee
Unfortunately, you cannot add a certificate to the trusted certificate authority on an Azure Web App. The security implications would be quite bad if that were possible.
However, what you can do is override the framework code for SSL verification to include your particular cert (for example in .NET this would be ServicePointManager.ServerCertificateValidationCallback). This stack overflow question and answer shows how to do that for .NET: How to call the default certificate check when overriding ServicePointManager.ServerCertificateValidationCallback in C#?