I think it would be easiest to get the index by the name using the built in list index property:
with arcpy.da.SearchCursor(fc, '*') as cur:
for row in rows:
print row[cur.fields.index('SITE_ID')]
It would actually more efficient to not have the index in the loop:
with arcpy.da.SearchCursor(fc, '*') as cur:
ind = cur.fields.index('SITE_ID')
for row in rows:
print row[ind]
This way it does not have to find the index inside each iteration since the index will not change.