Are there databases to annotate non-coding mutations? I would like to ask if there are some known databases that allows to annotate non-coding mutations in a given region for the human genome?

Preferably, if the database is downloadable so I am able to automatize the processes of annotation.
VarSome allows you to annotate any variant, including non coding ones. While ACMG classification will not be available if the variant isn't in a gene's transcript (the ACMG criteria are only applicable to variants in transcribed regions), non-coding variants in transcripts will be fully annotated. For example, if you look up variant chr17-41197559-G-T which is a non-coding variant found in the UTR of one of the transcripts of BRCA1, you will get a lot of information (probably best to click on the link, the image has a lot of data):



For non-coding variants that don't fall in any transcript, you can still get frequency data, when available, as well as DANN pathogenicity predictions, GERP score, an overview of the genomic regions and other variants and/or srtuctural variants that can be found around the region, and any community annotations that may have been submitted by other users. 

There is also an API you can use to automate the annotation, and VarSome Pro that lets you annotate an entire VCF file, but those are both paid services.



Disclaimer: I work for the company behind VarSome.