There is an answer to a related question on Science Fiction & Fantasy:
I don't believe that a reason was ever given. However, in light of the
other movies, I have a theory.
After the events in New York, SHIELD took the scepter for "safe
keeping". Most likely under Fury's orders to determine its threat and
other uses. Given that HYDRA had successfully infiltrated SHIELD at
this point, the scepter was "lost" somewhere along the way. Either
that, or HYDRA took advantage of the events in Winter Soldier to steal
the scepter. Although, I believe the first is more likely, seeing as
how Strucker had been experimenting on folks for a while. But, it
probably wasn't until after SHIELD/HYDRA collapse that it was realized
to be missing. This could be done by sending falsified reports about
anything going on with the scepter. Again, since HYDRA was at all
levels of SHIELD, this would have been fairly simple to do. Especially
since the head of SHIELD himself was HYDRA.
Sadly, this would have made a great Agents of S.H.I.E.L.D. episode,
and they missed the opportunity. There was pretty much no lead up to
the fact that HYDRA had the scepter, except for the tiny credits scene
for Winter Soldier.
And on Reddit:
I think the explanation comes at the the end of Winter Soldier.
Strucker in the mid-credits scene says that "it's worth more than any
of them ever knew." I assume the Avengers simply didn't realize how
powerful the scepter really was, so SHIELD just took it.