Note that the standard (POSIX/Unix) command to create a tar file is pax. pax combines the traditional cpio and tar commands.
To create a tar file, use the write mode:
pax -w < abc.txt > allfiles.tar
To copy instead, use the copy mode:
pax -rw < abc.txt Folder/
Note that it recreates the directory structure into Folder. If you want to flatten it, you could do:
pax -rws '|.*/||' < abc.txt Folder/
(see the man page if you want to copy permissions or other attributes as well. pax expects one file per line, which means files whose name contains newline characters cannot be copied that way, some pax implementations support a -0 option to allow a NUL delimited file list instead).
With cpio:
cpio -pd < abc.txt Folder/
With GNU tar:
tar -cf - -T abc.txt | (cd Folder && tar xf -)
Another option to allow any character in file names is (with GNU cp):
xargs cp -t Folder < abc.txt
(that flattens the directories).
xargs expects a blank (space, tab, newline) separated list, when you can escape those separators with backslash, single or double quotes. So you can have a list like:
"file with space"
other-file
'file with "quote" and
newline'