I referred to your profile and see a refrigerator listed with model number 12842116. Although this is not the model number, it is the part number for an owner's manual for Kenmore refrigerators beginning with model numbers 596.5565 . . . Using this information, here are some tips that should help you increase the water pressure in your refrigerator:
If you have not changed your water filter recently, I recommend changing it and checking to see if your water pressure increases.
If your water quality is good enough where you do not need a filter, you can install a bypass plug in the filter housing instead of a filter. You may have received this part with your refrigerator. If not you can order a new one. The part number for the bypass plug is 67003146. You can order this part from the Sears PartsDirect website
If the filter is not the problem, you may have a problem with water pressure or flow supplied through the line in the back of the refrigerator. Try cycling the water supply shut off valve that is in your house plumbing system. Sometimes, the valve is clogged with hard water deposits or debris. Cycling the valve may clear this type of restriction or clog. See if the water pressure improves. If not, shut off the water supply and unplug the refrigerator. Disconnect the water supply line on the back of the refrigerator. Place the end of the supply tube in a bucket and briefly turn on the water supply valve to check the pressure and the flow. If pressure or flow is weak, then I recommend calling a plumber to resolve this supply issue.
If water supply is adequate to the back of the refrigerator and the above tips do not help, then you could have problem with the water system inside the refrigerator. If your ice maker is working properly but your water dispenser pressure is low, you could have a frozen water line connecting to your water tank in the refrigerator. Check your refrigerator temperature and adjust it upward if it is too close to freezing.
Deposits in the refrigerator water system or a faulty solenoid water valve could also cause low water pressure.
If you need more help, resubmit your question with additional details and the full model number of your refrigerator.