This is now covered in Canon 351 § 1 of the 1983 Code of Canon Law. This Canon says:
“The Roman Pontiff freely selects men to be promoted as cardinals, who have been ordained at least into the order of the presbyterate [i.e., priest] and are especially outstanding in doctrine, morals, piety, and prudence in action; those who are not yet bishops must receive episcopal consecration [i.e., consecrated as a bishop].”
So it is now pretty straightforward. You have to be at least a priest. Since you need to be at least 25 years old to be a priest, this requirement, also, adds an implicit age requirement, i.e., 25. So the days of early-teen cardinals is now definitely history.
Canon 351 tightens the cardinalate requirements from the 1917 Code. That required priestly ordination, along the lines that the 1983 Code now requires episcopal consecration. In theory, this meant that if a cardinal was not a priest, he needed to be ordained. The 1983 Code on the other hand appears to stress that already being a priest is a prerequisite.
[I would think that a pope, if he really so wished, could override this as well as any of the other requirements — though I do not see this happening. However, it is worth noting that the need for episcopal consecration is sometimes waived by a pope, particularly in the case of those created cardinals late in life. Check this post about ‘non-bishop cardinals.]
Hope this helps. I had seen a number of searches of late with people looking for data on this topic.