12.B. The real numbers $a, b, c$ satisfy $a \leqslant b \leqslant c$, and $ab + bc + ca = 0, abc = 1$. Find the largest real number $k$ such that the inequality $|a+b| \geqslant k|c|$ always holds.
12. B. When $a=b=-\sqrt[3]{2}, c=\frac{\sqrt[3]{2}}{2}$, the real numbers $a, b, c$ satisfy the given conditions, at this time, $k \leqslant 4$.

Below is the proof: The inequality $|a+b| \geqslant 4|c|$ holds for all real numbers $a, b, c$ that satisfy the given conditions.
From the given conditions, we know that $a, b, c$ are all not equal to 0, and $c>0$.
Since $ab=\frac{1}{c}>0, a+b=-\frac{1}{c^{2}}<0$, it follows that $a \leqslant b<0$.
By the relationship between the roots and coefficients of a quadratic equation, $a, b$ are the two real roots of the quadratic equation $x^{2}+\frac{1}{c^{2}} x+\frac{1}{c}=0$.
Then $\Delta=\frac{1}{c^{4}}-\frac{4}{c} \geqslant 0 \Rightarrow c^{3} \leqslant \frac{1}{4}$.
Therefore, $|a+b|=-(a+b)=\frac{1}{c^{2}} \geqslant 4 c=4|c|$.