## Yes, if you have a magic item that does that

The problem, is that the rules on *PH* p. 151 that describe arcane foci say:

> An arcane focus is a special item— an orb, a crystal, a rod, a specially constructed staff, a wand-like length of wood, or some similar item— **designed to channel the power of arcane spells**

and you can read that to mean not any wand or staff can do that, only one designed to act as an arcane focus. 

And none of the wands or staffs in the *DMG* says it is designed to channel the power of arcane spells, or that it can be used as an arcane focus. This has been discussed in great detail in https://rpg.stackexchange.com/questions/59951/does-every-magic-rod-wand-crystal-orb-and-staff-count-as-an-arcane-focus.

Now, as you can see from the answers to that Q&A, not only is the overwhelming community consensus that you should allow such magic wands and staffs to be usable as an arcane focus, it also is the repeatedly documented designer intent that this is possible. 

In addition, if your DM designed a magic item like an *Orb of Fiery Death* that said it can be used as an arcane focus and adds +3 to your spell attack rolls for firebolt, then that would of course work too. 

By all means, if your DM allows it, use your magical wand as an arcane focus. We have been doing so in our group, and it has not caused any issues, to the contrary, we think it is much more fun this way. If your wizard finds an awesome [wand of the war mage][1] in their adventures, it would really suck if they could not use it as the wand they use for their focus, and instead would have to use a boring old normal wand, just because that one says it can be used. 


  [1]: https://www.dndbeyond.com/magic-items/34712-wand-of-the-war-mage