You can search the Apple App Store, but you won't find an app from Google for Google Docs. There are third-party apps, but nothing from Google. Except, that is, for the limited support for Google Docs hidden in the iOS Gmail app.
I found this by accident. I had a link to my Google Docs page in an e-mail I was reading in the iPad GMail app.
I clicked on the link and it opened a Docs tab on the GMail app. Below left is the file listing. Below right is a simple word processing document.
The only document support is for word processing and spreadsheets. The support is very, very, very basic--and buggy. There is, as far as I can see, no ability to perform even basic formatting tasks such as bold or italic.
The spreadsheet view below left is at about the same level of support as the word processing software. Both apps have a link to switch to the Desktop View, which seems to be Google Docs in the Web browser. If you select the Desktop View in the word processor you get an error message (below right). If you select Desktop View in the spreadsheet, you get a warning page that says the browser might not support all the features necessary for Google Docs.
These bits and pieces of Google Docs left in Gmail all have the look of something that was left in the app by accident. I tested it on my iPhone and that worked as well, which is to say badly--but it is good enough for a document viewer at least.