The concept of the Earth's orbit is extensible; bodies can rotate around the planet as far as 120 km. and 36 thousand km. from the surface of the Earth, but people most often fly to the International Space Station (ISS), whose orbit varies from 337 to 430 km, so we will consider the possibility of calling from an altitude of the ISS orbit.
Astronauts on the ISS constantly keep in touch with the Earth, using special radio transmitters, but is it possible to make a call from there on a regular mobile phone? If you give a short answer, then no, in the normal mode of operation of the mobile network, it will not be possible to call into orbit, the system is configured to work with devices on the surface of the planet, but with relatively minor changes in the equipment settings, the astronaut will be able to use the phone. To understand how to do this, you need to understand some of the principles of mobile communication.
How mobile communication works.
Base stations and mobile phones operate in the frequency range from 890 to 960 MHz. Waves of this range pass well through the ionosphere and easily reach equipment in orbit, in contrast to the long waves that bounce off the ionosphere. The station sends data in packets, after each packet it waits for a response signal for a certain time and if it does not receive it, it starts working with another phone. On flat terrain, it is precisely this waiting time that limits the range of the base station, but it can be adjusted and, with proper tuning, it will be enough for the signal to reach the phone in orbit and return back.
Large base stations on Earth have sufficient power to transmit a stable signal over a distance of 120 km or more in clear weather, the range of their operation is artificially limited, for greater network efficiency, and because, due to the curvature of the Earth's surface, there is simply no point in sending a signal even further. The exact characteristics of base stations depend on the manufacturer and model, I could not find data on the most powerful station, but those about which I managed to find out are capable of providing communication at an altitude of 150 km, and if you remove the power limiters and squeeze the maximum out of them, these stations are quite capable transmit a signal to the ISS orbit, provided that the antennas are directed upward.
What's the problem with making a call from orbit?
The difficulties of making a call from orbit are related to the power of the transmitter in the mobile phone and the speed of its movement in orbit. To transmit a signal to Earth from the ISS from the phone, you have to squeeze out the limit of its power, at which it can work for a very short time before it burns out, however, it would be enough for a short conversation. But a much bigger problem is the tremendous speed at which spaceships move in orbit. Because of it, the phone will be in the coverage area of the base station for only a few seconds, and the higher the orbit, the shorter this period of time will be. Usually base stations have a restriction on exchanging signals with fast moving objects, this restriction must be removed in order to make a call.
Thus, if you properly configure the equipment, you will be able to call a phone located at an altitude of 150 km, however, the conversation will be regularly interrupted due to switching the device between base stations, making a call to the ISS will already be extremely problematic, since its orbit is on the border the range of the base station and mobile phone, as well as switching between base stations will occur very often, which will make the conversation almost impossible.