It can. Radio signals induce currents and voltages in conductors and semiconductors (how a radio receiver picks the signals up). When you are making a very sensitive measurement, you need to have what is called a low signal-to-noise ratio, and those induced currents are added noise in DC circuitry that measures a scale's transducer output. Put enough such current into a semiconductor junction such as the input transistor to an operational amplifier measuring a strain gauge, for example, and it can create an offset voltage that is added to the reading and shows up as a measurement error. The only way to block this is with a Faraday shield, and the higher price scales have them built-in. You can use an aluminum foil-lined box if you need to improvise one.
The other common way radio frequency interference (RFI) gets into electronics is when the noise source, like electric motor brushes in your blender motor or the current surges in a fluorescent lamp fixture, draw that interrupted and surging current through the AC line and they enter a plugged-in power source in your scale. In that instance, using an RF filter on your power connection can help. These are built into computer battery-backup devices, and if you have an old one, even with no battery, you can plug it into the wall and then plug the scale power into it to get that filtering.
But before you go to any of this sort of trouble, make sure you have a problem. Turn off the fluorescent light and motors. Turn off the cell phone to power it down. Wrap it in foil. Take a reading. Bring the phone back and see if the scale reads the same.