After fumbling attempt after attempt at getting social networking right, Google is looking for a new executive to show it the way. It’s apparently hiring a new head of social.

GigaOm obtained a recruiting letter describing the position:

“This is a new and very strategic position, as Google knows it is late on this front and is appropriately humble about it. In Google’s view, conceptually, there are two ways to tackle social, each impacting who may be successful in this senior post: 1) building an innovative offering specifically in this area; or 2) developing the capability and integrating social into Google’s existing portfolio.”

Google wouldn’t confirm whether it’s looking for such a person except to say: “We’re continuing to invest heavily in people and are recruiting top talent in all areas of the company.”

This is a particularly sensitive time for the company’s social strategy after Facebook unveiled its concept of an Open Graph last month, a map of all people relationships between each other and to the things they care about.

That is a definite threat to the way Google ordered the web over the past 10 years by analyzing links between pages. With Facebook’s “like” button and and social plug-ins now strewn across tens of thousands of sites, it’s only a logical hop, skip and a jump to a distributed advertising network and competitor to AdSense. Facebook has not made any definite announcements on additional advertising schemes, however.

While Google has a whole suite of products that are social from Orkut, the network that’s popular in Brazil and India, to Google Buzz and newly-acquired social search service Aardvark, it has yet to form a coherent strategy in the area. The closest thing Google has to a social guru may be vice president of product management Bradley Horowitz. It also recently hired Joseph Smarr away from Plaxo and open web advocate Chris Messina to help guide the company’s way.