That is a good question. As you will know, silk and some other materials, such as spider silk or even synthetic fibers such as Kevlar (which is used in bulletproof vests), are in some sense "stronger than steel". In this specific case, it means that the tensile strength (ability to resist a pulling force) of a fiber PER WEIGHT is larger for silk than for steel. This is remarkable and from the case of Kevlar you can see how that can be technologically useful: Kevlar bulletproof vests have so to speak replaced the iron garments of the knights of the Middle Age, and are outperforming them.

When it comes to replacing the steel in reinforced concrete, however, several other issues need to be addressed. These are mostly of a very practical nature, engineering issues in a sense. A very crucial one is the question of availability. Silk fabric is expensive, which is the case because silk is a precious material, originally coming from silkworms spinning it for their cocoons. While this is not the only source anymore, silk still is a biological material and much harder and more expensive to produce than steel. The biological nature of silk, being a protein, also gives rise to other problems: one would have to find a way to prevent the embedded silk from rotting, getting attacked by mold, being damaged chemically by the concrete and so on. So I think that it would be practical matters like these that would prevent silk from ever being used to reinforce concrete on a sizable scale.

Even synthetic high strength fibers such as Kevlar, which are easier to produce than silk are too expensive to replace the steel, simple because such huge amounts of reinforced concrete are used in the world. However, there may be applications of the concept that you suggested on a much smaller scale.

I actually just read an article where researchers used the silk protein in combination with another protein that is involved in the biomineralization of silica to make a precursor of reinforced concrete on the nanoscale! Which means that there are certainly applications for creative thoughts like yours...

It is not possible to replace the steel with silk. Silk can take a heavy tensile load (you can hand a weight from silk fiber) but silk cannot take a compressive load. The steel in concrete can take a compressive load, meaning that you can place weight on steel, and it will take the weight. You cannot do this with silk. So steel is still better for concrete.