Edit
Since answering additional services have become available, although I have not personally tried some of them, they may suit this purpose.
https://learn.microsoft.com/en-us/azure/search/cognitive-search-concept-intro
And at some point in the future when It goes GA.
https://aws.amazon.com/textract/
Original Answer
Unfortunately Azure has no PDF integration for it's Computer Vision API. To make use of Azure Computer Vision you would need to change the pdf to an image (JPG, PNG, BMP, GIF) yourself.
Google do now offer pdf integration and I have been seeing some really good results from it from my testing so far.
This is done through the asyncBatchAnnotateFiles Method of the vision Client (I have been using the NodeJS Variant of the API)
It can handle files up to 2000 pages, Results are divided up into 20 page segments and output to Google Cloud Storage.
https://cloud.google.com/vision/docs/pdf
For PDF and TIFF files, up to 2000 pages (only first two pages for the free tier) are processed.
learn.microsoft.com/en-us/azure/cognitive-services/… – Geralyngeraniaceous