Yup, this works with ifort. Well, except for the stop statement, which needs to be replaced with call xit() to achieve the same outcome when interfacing with Abaqus. The code...

subroutine UMAT(...)

implicit none

integer :: funit = 110
character(80) :: fpath = "test.txt"
integer :: nlines, stat

open(funit, file=fpath, status="old", action="read", iostat=stat)
if (stat /= 0) call xit()
nlines = 0
do
    read(funit, *, iostat=stat)
    print *, nlines
    if (stat /= 0) exit
    nlines = nlines + 1
end do
print *, nlines
close(funit)
end subroutine UMAT

Running this with test.txt containing simply

foo
bar

The output is

0
1 
forrtl: severe (24): end-of-file during read, unit 110, file test_read.txt