It's a physical impossibility for an air conditioner to add moisture to the air, but it can fail to dehumidify the air if it's cooling coils aren't running cool enough (below the dew point of the room air.)
When comparing weather data to interior air don't look at
relative humidity, look at the dew point. Relative humidity is a meaningless number without the associate
temperature it's relative to- it's simply a measure of how close the air is to saturation. But the saturation level varies with the temperature of the air. The absolute humidity or moisture content is measured by the dew point.
Say the outdoor air is 90F and 30% RH outside, the outside dew point is ~55F- cool that same 55F dew point air (without removing or adding moisture) to 75F and it's relative humidity becomes ~50% without any change in the moisture content. Cool that same air down to 55% and it's at 100% relative humidity. Same air, only the temperature changes.
You can get this info off a
psychrometric chart, or use an
online psychrometric calculator.
But since the cooling coils on the AC unit SHOULD be well below 55F, water should be condensing on them, drying out the air. At it's lowest blower speed, try to measure the output air temp with a bulb thermometer. If it's putting out air no colder than 60-65F air at low speed it's likely the refrigerant charge or volume control is off. At lowest blower speed the coil runs cooler, which condenses more water out of the air, but some high SEER models at high speed don't do much drying at high fan speed.
FWIW: 50% RH @ 75F is a perfectly healthy indoor humidity, but above 60% it's less comfortable, and fungus/mold risks begin to rise. Those with dust mite allergies are advised to keep it at 50% or lower, since dust mites can't reproduce at that humidity level, but most people are just fine up to 60%.