Yes, ANNOVAR supports hg38/GRCh38. You just have to install the databases by downloading them. Take a look here: http://annovar.openbioinformatics.org/en/latest/user-guide/startup/
annotate_variation.pl -buildver hg38 -downdb -webfrom annovar avsnp147 /Programs/ANNOVAR/database/humandb/
This will download dbSNP version 147 with hg38 co-ordinates to a directory called /Programs/ANNOVAR/database/humandb/. You can have multiple databases on your computer for each of hg18, hg19, and hg38.
When you then execute a further command to actually annotate variants make sure that you always use
-buildver hg38 in the command, but you can flexibly use
-buildver hg18 and
-buildver hg19 if you have those installed too and also depending on the genome build of your data.