Unfortunately, it is not possible to download Adobe Acrobat Reader Portable. Adobe does not offer any version of its software that can be carried on a Pendrive. If you search the Internet, you will see lots of results, but we are sorry to inform you that these versions are mostly fakes, and there is no way to know what they contain (including malware).
What you can find, if you know where to look, are modified versions ready to be executed without installation, although its legality is highly questionable. However, since it is a development made by enthusiasts and independent developers, there is no guarantee that it will work.
In this particular case, it is necessary to talk about alternatives that can work as portable programs and can work with PDF files. Regarding this, we can recommend two programs: SumatraPDF and Foxit PDF Reader. Both are the two best possible options to replace Adobe Acrobat Reader, and you can take them anywhere on a USB drive.
If these two options do not make it for you, you can try free office suites, such as OpenOffice and LibreOffice, since they let you work with PDF files and can also be found in a portable format. However, if you can get a native PDF reader, do it
If at any time, Adobe decides to release a portable version of Adobe Acrobat Reader, we will be the first to tell you about it. But until that happens, here are a few alternatives to you.