According to the following Wikipedia page,
you can update the operating system on your iPhone 3GS to iOS 6.1.6.
Since Acrobat DC for iOS requires iOS 8 or newer, you are not able to install Acrobat DC for iOS.
However, the Apple App Store detects your iOS version and provides the latest compatible version, which is Adobe Reader for iOS (the older version).
Would you try downloading it from the App Store?
Please let us know if you have trouble downloading and installing Adobe Reader for iOS on your iPhone. Thank you.