The other answers say that this isn't possible in the way that you want to do it, but they don't provide the equations that show why.
Deflection of a Cantilever
The equation for the deflection of a cantilever beam:
$$ \delta = \frac{FL^3}{3EI} $$
Where: $F=Force \\
L= \text{Length of cantilever} \\
E=\text{Modulus of Elasticity} \\
I=\text{Moment of Inertial}$
As you can see, none of these components have anything to do with strength. The only variable that is affected by the material is $\text{E}$. This is basically constant for steels.
Column Strength
You didn't necessarily ask about the material strength of your tube though. You asked about replacing a strut. A strut is a column. The compressive capacity of a column is ultimately controlled by Euler Buckling (hint: it rhymes with "oiler").
$$F=\frac{\pi^2EI}{(KL)^2}$$
Where: $\text{K is dependent on the end connections} \\
\text{(well, see above, everything else is the same)}$
This also shows that buckling capacity isn't dependent on material strength. Assuming that the original solid bar is the same material as your replacement tube, there is only one parameter to compare $\text{I}$, (Moment of Inertia).
Take the diameter of your original solid bar and use that to determine the the required diameter and thickness of the wall so that the moments of inertia match.
What if the materials are not the same?
It the materials are not the same, then the E value will change. Everything else in the equations stays the same, so EI will need to stay the same. The moment of inertia may go up or down depending on how the modulus of elasticity changes.
This ends up meaning that a stiffer strut will have a greater EI. This also contributes to a higher buckling force. If buckling is the controlling failure mode, then a strut that deflects less will be stronger.
Note: Insert standard warnings about there being lots of other factors that could affect this. Don't use this for things related to human life or anything that you care about.