Try this (it's crude but it works). Save it as a lsp file like "DimArc.lsp" then load it in AutoCad using the Tools menu or (Load"DimArc"

on the command line, then run it by typing DimArc on the command line.
;
(DEFUN C

imArc (/ p1 p2 p3 p4 om ang rad arc ark) ; Dimension an arc
(SetVar "CMDECHO" 0)
(Setq om (GetVar "OSMODE"

)
(setq p1 (getpoint "\nSnap to first point (must be on the arc also): "

p2 (getpoint "\nSnap to second point (does not have to be on the mark): "

)
(COMMAND "Osnap" "CEN"

(setq p4 (getpoint "\nPick a point on the connecting arc: "

)
(COMMAND "Osnap" "NON"

(setq p3 (getpoint "\nPoint to dimension location: "

ang ( - (angle p4 p1) (angle p4 p2))
rad ( distance p4 p1)
arc ( abs (* rad ang ))
ark (rtos arc)
)
(COMMAND "DIM1" "ANG" "" P4 P1 P2 P3 ARK P3)
(COMMAND "DIM1" "HOM" "L" ""

(COMMAND "DIM1" "TE" "L" PAUSE)
(SetVar "OSMODE" om)
(princ)
)
;