Or add a data point or two and use a TEXT plot.
proc sql;
create table work.myclass as
select age,height,mean(height) as mHeight
from sashelp.class
;
quit;
data work.label;
age=14.2;
y=70;
Labeltext= "The Reference Line";
run;
data work.plot;
set work.myclass
work.label;
run;
proc sgplot data=work.plot;
scatter x=age y=height/ name='scatter';
refline 14 /axis=x labelloc=inside label="" lineattrs=(color=green);
text x=age y=y text=labeltext /rotate=90 name='text';
keylegend 'scatter';
run;
Changing the Rotate angle to =90 will make it read from top to bottom. Adjust the x and y coordinates to be "nice". There are also some text appearance options available with a Text plot, such as BACKLIGHT not available in REFLINE.