Was Alaska once connected to Russia?

Yes it was.

Scientists have a theory that Russia was connected to Alaska by a land bridge called Beringia (a place that existed during a time when much of Canada was covered in massive sheets of ice) but that was long ago and just a theory though.

The Beringian land bridge is believed to have existed both in the glaciation that occured before 35,000 years ago and during the more recent period 22,000 to 7,000 years BP (Before Present).

Conclusion: It was just a theory but it might be true cos glaciation truly occured in the past and through that glaciation, a connection between Russia and Alaska happened.