We haven't yet made a serious attempt to deflect an asteroid. But there are many technologies we can use given enough warning.
We can paint one hemisphere white for instance, or use a spacecraft orbiting it as a gravity tractor, or attach a weight (e.g. spacecraft) to it on a long tether which would change its orbit, by a tiny amount but enough to deflect it away from the Earth months or years later.
That works because a tiny effect, which acts on its orbit continuously for months or years, can move it by thousands of kilometers. Especially, should be easy to divert an asteroid if it has multiple flybys of Earth before the predicted impact (which would be the usual situation) where a tiny change in position of entry into the Earth Moon system can have a big effect on its trajectory after that.
It wouldn't be possible to do much about an incoming tiny object that we detect only say a day before impact. In that case best thing would be to plot its trajectory carefully, and if it is headed for an inhabited region, warn everyone to stay indoors and keep away from windows in case of flying glass - or in worst case to evacuate.
The chance of a damaging impact are much less than most think. And we have programs underway to detect small asteroids.
An asteroid as small as the Soyuz though would not be considered enough of a threat to try to plot them. It will probably burn up in the atmosphere most of it. Some may make its way down to the ground. The same is true for meteorites. Many of those make their way down to the ground, but it is rare for them to cause any damage.
There is a famous example of this car that was hit by an asteroid, the Peerskill asteroid.
In the case of the Soyuz and other spacecraft, the parts most likely to survive are spherical components, the so called "space balls".
Believed to be a pressurant sphere from a Soyuz Progress vehicle.
There have been many of these fall to Earth over the last several decades, result of all the space launches. So far, as for meteorites , nobody has been hit by any of them.
Ideally you would target spacecraft and final stages to land harmlessly in the middle of the South Pacific where there is nothing but ocean.
But we take up far less of the surface of the Earth than you'd think. Most of the surface is uninhabited, or sparsely inhabited: ocean, glaciers, ice caps, permafrost, deserts, mountains.
In regions that are inhabited, still, humans occupy much less of the surface area than the fields of our agriculture, and our houses and roads, machines, cars etc.
SOME LINKS
Entertaining TED talk about asteroid impacts and what we can do
One of several blog posts about one of the many meteorite scare stories (we get them every year or so, and sometimes they are published by large distribution newspapers that should know better) by Phil Platts - there's a nice video debate with experts about asteroid impacts at the end