The peak tension is at the geostationary point, and is about 50,000 kNm/kg. This has the units of the sound speed in the material squared.
Send a nuclear powered robot to the asteroid belt, find an appropriate sized carbonaceous chondrite asteroid. We're talking ~300 m long. Have it mine water and blast it out to move its orbit to the Earth, inserting it in geostationary orbit. Construct a cable by extrusion, probably pointing away from the earth. When it's finished, rotate it into place above a suitable point on the Earth. Profit. Problems include possibly crashing said asteroid into Australia, and a slow rate of construction. Even if it built a cable at 1 km/day, it would still take 100 years to reach the required length.
Question: What would it look like?
Discussion: Not much. At any point along its length, perspective would disappear it out of sight within a few km. On the earth's surface, it would appear as a rope going up and disappear from sight before reaching the clouds. From the top looking down the earth would be the size of a basketball at arms' length. On the way down, the earth would appear to dominate the view with a horizon for the whole day, but only in the last half hour would you enter the atmosphere. For comparison, it has similar length-width ratio with a railway rail that stretches across a continent.