You can unclog a toilet without a plunger by placing a combination of soap and hot water into the clogged toilet. This process may require repetition as well as the use of an unraveled wire to push debris down the toilet pipe.
Because it requires adding water and soap, this process only works on a toilet that is not overflowing. If the toilet is overflowing, excess water needs to be removed before this technique can work.
Begin by squirting large amounts of dish soap into the toilet. If dish soap is not available, cut off pieces of bar soap. Afterward, add a gallon of hot water to the toilet bowl. The water should be hot but not boiling. After a few minutes, the hot water should break up the toilet paper that is clogging the toilet, and the soap should help that toilet paper slide down the pipe. If initial results are unsuccessful, you may need to add more soap or add more hot water, if possible.
If this method is still unsuccessful after multiple attempts, contact a professional plumber to deal with the toilet or consider purchasing other specialized devices, such as a closet augur, to deal with the clogged toilet.