Is there a standardized (meta?) tag for the date of a website?

It's not a standard, but I remember reading on A List Apart about RDFa. It, or other forms of microformatting, may just be the solution you're looking for.

There have been a few WHATWG Meta Extension proposals, referenced in the HTML5 specification which could cater for the creation date of a page.

"Accepted" Proposals
dcterms.available - The date the resource became available.
dcterms.created - The creation date of the resource.
dcterms.dateAccepted - The date the resource was accepted.
dcterms.submitted - The date the resource was submitted.
dcterms.issued - The publication date of a resource.

Related "Accepted" Proposals
dcterms.modified - The modification date of a resource
dcterms.valid - The validity of the resource.

There are a couple of "incomplete proposals" which haven't been accepted due to a lack of documentation (such as created).

I don't believe Hangy's answer of dc.date (now dcterms.date) would be relevant here as, as far as I'm lead to believe, the date of this is the date associated with the resource. For example, if the resource was a discussion about the Battle of Hastings in 1066, the dcterms.date could be set to 1066. The same could also be said for icas.datetime.

You could try RDFa (or Microformats) as James and hangy have suggested, Google supports them through a feature called Rich Snippets. Use the Rich Snippets Testing Tool to see how it's working - for example it does pick up the dtreviewed and the rating from one of my blog posts which is marked up with hreview.

I suppose the DC.date tag could be used for that. The Dublin Core metadata is relatively established and well known.

You could also mark your websites with XMDP, which has a date tag that is supposed to be the date of the last modification.