Edit: I came across this old answer and was amazed (actually shocked) how inefficient and complicated solutions I suggested.
A much better approach: Since gnuplot 5.2.0 you can index datablocks. Prerequisite is that your data is in a datablock already. See here: gnuplot: load datafile 1:1 into datablock.
If you can be sure that your data files have identical number of lines, you can "mimic" the Linux paste
command using a gnuplot-only, hence, platform-independent solution.
Basically, you join the two lines having the corresponding index after removing the last character (newline) of each line.
Script: (works with gnuplot>=5.2.0, Sept. 2017)
### plot arrows across two files, i.e. merge lines with gnuplot only
reset session
$Data1 <<EOD
File 1
x y
1 2
5 4
4 6
EOD
$Data2 <<EOD
File 2
x y
5 6
3 4
2 3
EOD
set print $Combined
do for [i=1:|$Data1|] {
print $Data1[i][1:strlen($Data1[i])-1].' '.$Data2[i][1:strlen($Data2[i])-1]
}
set print
plot $Combined u 1:2:($3-$1):($4-$2) w vec lc rgb "red"
### end of script
Result:
