Not directly with fmriprep-docker, but when you run fmriprep-docker, it prints a fully-expanded command, e.g.
$ fmriprep-docker /bids /bids/derivatives participant -w /scratch
RUNNING: docker run --rm -it \
-v /bids:/data:ro -v /bids/derivatives:/out -v /scratch:/scratch \
poldracklab/fmriprep:1.1.1 /data /out participant -w /scratch
(Newline and spaces added for readability.)
So you can copy this command, and make additions such as -u $UID, which will cause it to run under your user name:
docker run --rm -it \
-v /bids:/data:ro -v /bids/derivatives:/out -v /scratch:/scratch -u $UID \
poldracklab/fmriprep:1.1.1 /data /out participant -w /scratch
Note that you’re going to need to use the -w flag and mount a working directory that you own into the container, to avoid permission issues within the container.