Would it be possible to send a text to someone on Earth from the ISS using a standard cell phone?
Yes, and no. Let's examine the no part first, then I'll explain the yes.
A regular cellphone, the one most people think of when you talk of a cell phone, use cell towers that point sideways and slightly downward. The distance to the ISS, over 300 km, is too far for both the transmission power and the transmission protocol; if the tower could receive a signal it would try to disregard it as interference and it isn't powerful enough to transmit that far to a standard internal cellphone antenna.
The International Space Station orbits in a low Earth orbit between 330 and 410 km.
The Burj Khalifa is by far the world's tallest structure at 828 metres (2,717 ft); while it is said to have "communications equipment" on the spire it's not clear that there are cellular antennae installed. It's less than one kilometer tall in any event.
Quora has a Q&A: "What's the highest altitude you can still get cellphone service from a cell tower?", which is answered: 'using a GSM phone, 35.406 km (116,160 ft)' and "... in New York, people have issues making cellular telephone calls from the top of a skyscraper. (because the tower's antennae don't point upward)".
A cell phone booster will only get you 32.187 km (20 miles).
There is 4G coverage on Mount Everest, but it's at 5,200 metres above sea level.
All of the above means no.
But what is to follow means yes.
IF your definition of "a standard cell phone" includes a "satellite phone" then you are in luck, afterall the ISS orbits at satellite altitude; what would you expect.
There are basically two means of using satellites for communication by phone, some satellite phone satellites orbit at low Earth orbit (same as the ISS) so the "distance" is relatively short. Other satellites orbit geosynchronously, which places their downward pointing antennae above the ISS. Either way you should expect them to work, with the geosynchronous orbiting satellites providing longer (probably constant) reception.
Here is what a satellite phone looks like:
Not much different than a 4G phone, except for the tiny external antenna, and the U\$1300 price tag; though used phones cost ~U\$200 and up. The Iridium Extreme 9575 is their top of the line model so the price isn't too bad, what you need to know (don't want to know) is how much per minute it costs to use.
But you want to use a regular phone you say, how about a phone like this:
Yes. How about a laptop, a fax machine, ISDN, yes: The Hughes 9202 BGAN Terminal is 21.6 x 21.6 x 4.6 cm (8.5″ x 8.5″ x 1.8″ inches) and as a hotspot supports up to 10 concurrent wireless connections. That means 10 standard cellphones can communicate simultaneously with the ISS using this device:
You wouldn't need quite so fancy a device aboard the ISS since you'd be much closer than a Terran.