No, there is no cloud based version of Acrobat. Adobe does offer some online services of features that are also in Acrobat, but you will not find a complete replacement for Acrobat in the cloud.
You can convert to and from PDF using ExportPDF and the PDFPack, you can sign PDFs with EchoSIgn, you can create forms using FormsCentral, but other than that, you need Acrobat installed on your desktop to use Acrobat's functionality.
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