In this study, three fascinating resorcin[4]arene‐based Cu(I) complexes, named [CuCl (TPC4R)] (1), [CuBr (TPC4R)] (2), and [Cu2I2(TPC4R)] (3) were prepared by using a pyrimidine‐functionalized resorcin[4]arene ligand (TPC4R). In 1 and 2, two Cu(I) ions were linked by two TPC4R and two Cl− (or Br−) anions to form binuclear units. The adjacent units were extended into supramolecular layers through H bonds. In 3, two Cu(I) ions were connected by one TPC4R and two I− anions to form a mononuclear complex. The mononuclear units were connected by hydrogen bonds to produce a supramolecular chain. Significantly, 1 and 2 exhibit high efficiency and universality for azide‐alkyne cycloaddition reactions in the synthesis 1,2,3‐triazoles and β‐OH‐1,2,3‐triazoles. It has been found that the amount of catalyst, solvent type and reaction temperature have considerable influences on the activities of catalytic systems. The conversions of catalysts 1 and 2 could reach 99% for most of the selected substrates. It was found that after repeatedly used for 4 times, the catalytic activity of 1 did not decrease apparently.