This is almost impossible. You could leap across the Bering Strait from iceberg to iceberg. However, this is harder to do since the ice floats and weaves around it. It’s hard to get a straight line from Alaska to Russia. Even if you could get from Alaska to Russia across the Bering Strait - whether by walking across the thin ice that breaks easily or by leaping from berg to berg - no westerner can legally land by foot on Russia’s border with the Bering Strait.
If you make it, you will most likely be arrested as soon as a Russian soldier or policeman catches you.
However, way back in the days of Pangea, you could have walked from Russia to Alaska, or vice versa.
Yes, if that's what takes your fancy. You'll just need to be pretty careful tiptoeing across the Bering Strait, an icy path 35 km wide and often broken by ice floes, depending on the wind direction and tides. The strong current flows north through the strait, causing channels of icy water, often large.
But never mind, you can leap from ice chunk to ice chunk. There's one major problem you might want to consider: it's probably illegal to step onto Russian soil. You might not be welcome and you might be near death's door after your efforts.