3-terminals magnetic tunnel junction
You should be able to make a structure where the top FM layer is pinned, and the orientation of the magnetization in the bottom layer can be changed by the direction of current flow between your nodes 1 and 3. This is basically how MRAM bits are programmed.

But the current from node 2 to node 1 or 3 will be much, much less than the current needed to change the magnetization...this current must tunnel through the insulator.

So, in some sense of the word "transistor" you could make something kind of like a transistor. But it will have a current gain much less than 1, and it may be very slow compared to normal transistors of the same size.