Place apricots in a heatproof bowl. Cover with boiling water and let stand for 5 to 10 minutes to soften. Drain and rinse, then drain again.
Combine apricots, rhubarb, and sugar in a pot. Cover and let stand at room temperature until fruits release their juices, 8 hours to overnight.
Inspect 6 half-pint jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until jam is ready. Wash new, unused lids and rings in warm soapy water.
Bring apricot-rhubarb mixture to a boil over medium heat. Reduce heat to medium-low, cover, and simmer until rhubarb is tender and starts falling apart, about 3 minutes. Stir in pectin and bring mixture to a full rolling boil on high heat. Boil for exactly 1 minute, stirring constantly. Remove from heat. Skim off any foam with a ladle or a large spoon.
Pack rhubarb-apricot jam into the prepared jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any spills. Top with lids and tightly screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 10 minutes.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart. Let rest for 24 hours without moving the jars. Gently press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area.