Repairing Hairline Cracks In A Concrete Wall

Wash out the crack using water or air to remove any surface flaking and to remove any dust, dirt or grime from inside the crack. The paste will not adhere to dust, dirt or grime. You do not want to use a wire brush until the crack is smooth, the paste will adhere to a rough surface better than a smooth surface.
Wash the surface of the concrete, about 3 inches on both sides of the crack using water and a wire brush to remove any flaking paint, dirt or grime that may be on the wall. You do not want to capture any loose particles under your putty knife or pointing trowel while you are filling and smoothing the paste.
Using a spray bottle apply a mist of spray to the inside of the crack, continue to do that for about 3 hours or until the concrete has a darker color and appears to be wet. There should not be any droplets of water inside the crack. It is important that the concrete is wet, if it isn't, it will suck the moisture out of the paste and the paste will not cure properly.
Mix the Portland cement (pure Portland cement, not mixed with any sand or aggregate) into the water, adding a little at a time, until you have created a very smooth paste, having a consistency similar to tooth paste.
Fill the hairline crack, using a pointing trowel, putty knife or cake icing decorating bag, starting at the top and working down. Force the paste into the crack as deeply as you can.
Using a putty knife, smooth the paste so that it is flush with the surface of the wall.
Let stand for about 3 hours and then cover the crack with plastic and tape both sides using masking tape or duct tape to the wall.
Once a day, open the plastic and using a spray bottle dampen the patched area with water, and then reseal the plastic. This will allow the paste to dry properly, from the inside out and cure to a solid, very hard filling.
If you are planning on painting the patched area, follow the paint manufacturer's instructions for surface preparation of new concrete.