Friedel Crafts reaction of anisole Does anisole undergo friedel-crafts reaction or does the oxygen atom complex with Lewis acid?

We know that yields of this reaction are reduced in case of phenol but does the same happen in anisole?
It does indeeed.
This reference describes the F-C reaction of anisole under AlCl3 or BF3 catalysis in good yields with the expected o/p direction.
J. Am. Chem. Soc. 106(1984) 5284

There are numerous other references

It should be noted that Anisole + AlCl3 is a method for demethylation to the phenol.