I'm trying to catch up on my homework for earth science, but I'm having a difficult time searching for an answer to my question.
Zircons from Australia at 4.4Ga, and perhaps basalts from a Canadian island at 4.5Ga.
It would interest you to know the quest of Boston University geochemist Matthew Jackson, who is searching for the oldest basalt and mantle rock that exists.
His work isn't entirely agreed upon, as they are using all kinds of difficult isotopes which are a subject of controversy. Probably the most current information on early basalts are the claims and counter claims relating to Matthew Jackson in published articles, which have a lot of chemistry in them.
"We've been looking for pieces of the mantle that might have survived the chaotic mixing and churning within the deep Earth," said Boston University geochemist Matthew Jackson.
"We found rocks that reached the surface some 62 million years ago—suggest a whole reservoir of the primordial rock could still lie somewhere beneath the Arctic"
There are moon basalts from 3.7 Ga years ago, they are a bit mysterious, and lunar plagioclase feldspar at 4.5, appear to have formed when feldspar crystallized and floated to the top of a global magma ocean that surrounded the Moon soon after it formed.
Just what @comprehensible said, zircons from Jack Hills were the earliest materials (4.4 Ga) indicating that continental-type igneous rocks are already present on Earth during this period. Note that these zircons are found within metamorphosed conglomerate beds.
However, if we are talking about rocks (aggregates of material), then the Nuvvuagittuq greenstone belt (more or less 4.28 Ga) in Canada represents the oldest known crust, which also gives us the oldest rocks on Earth.
I remember watching a documentary years ago about diamonds and the places they are found in southern Africa. Apparently they are inclusions in the oldest rocks in that continent, which you could say fill up some sort of very large chimneys in younger rock, going vertically straight down.
So there you would have at least some of the oldest rocks on the planet.
The previous answer about the evidence of oldest crust is correct but if you are looking for the oldest igneous rocks that is a metamorphosed granitoid that formed 4.2 billion years ago. According to Wikipedia, the Acasta Gneiss is a tonalite gneiss in the Slave craton in Northwest Territories, Canada. The rock of the outcrop was metamorphosed 3.58 to 4.031 billion years ago and is the oldest known intact crustal fragment on Earth.