A birch is a thin-leaved deciduous hardwood tree of the genus Betula in the family Betulaceae, which also includes alders, hazels, and hornbeams.

It is closely related to the beech-oak family Fagaceae.

The genus Betula contains 30 to 60 known taxa of which 11 are on the IUCN 2011 Green List of Threatened Species.

They are a typically rather short-lived pioneer species widespread in the Northern Hemisphere, particularly in northern temperate and boreal climates.

Birch species are generally small to medium-sized trees or shrubs, mostly of northern temperate and boreal climates.

The simple leaves are alternate, singly or doubly serrate, feather-veined, petiolate and stipulate. (source)

So can guinea pigs eat birch?

Yes they can, it is fine for them to chew on.

Guinea pigs love to chew on tree branches to grind their teeth and birch is of no exception to this.