What is the complete reaction for Cyanide ions reacting with Thiosulfate?
Source 1(If you consider $\ce{Na+}$ as counterions)


$$\ce{Na2S2O3 + NaCN -&gt; Na2SO3 + NaSCN}$$


  Sodium thiosulfate reacts with sodium cyanide to produce sodium
  sulfite and sodium thiocyanate.



Source 2(If you consider $\ce{Ag+}$ and $\ce{Na+}$ as counterions for cyanide and thiosulfate ion respectively)


$$\ce{AgCN + 2Na2S2O3 → Na3[Ag(S2O3)2] + NaCN}$$


  Silver(I) cyanide react with sodium thiosulfate to produce sodium
  dithiosulfatoargentate(I) and sodium cyanide.


In this case, thiocyanate does not form, rather a complex forms.

Explanation of this reaction can be found by observing the related reactions given in the Wikipedia article of sodium thiosulfate.


  Silver halides, e.g., AgBr are typical components of photographic
  emulsions, dissolve upon treatment with aqueous thiosulfate:
  
  $$\ce{2S2O3^{2−} + AgBr → [Ag(S2O3)2]^{3−} + Br^{−}}$$


Since, $\ce{CN-}$  and $\ce{Br-}$ hold same charge,  you can easily replace it with silver bromide with silver cyanide  to get  cyanide ions as products.

Furthermore:


  Sodium thiosulfate is a component of an
  alternative lixiviant to cyanide for extraction of gold to form a
  strong soluble complex $\ce{[Au(S2O3)2]^{3−}}$. The advantage of this
  approach is that thiosulfate is essentially not toxic and that ore
  types that are refractory to gold
  cyanidation (e.g. carbonaceous or Carlin-type ores) can be leached by
  thiosulfate. Some problems  include the high consumption of
  thiosulfate, and the lack of a suitable recovery technique, since
  $\ce{[Au(S2O3)2]^{3−}}$ does not adsorb to activated carbon, which is
  the standard technique used in gold cyanidation to separate the gold
  complex from the ore slurry.


This process is also suitable for silver extraction using sodium thiosulfate and silver cyanide to form corresponding silver complex, $\ce{[Ag(S2O3)2]^{3-}}$. Just replace gold cyanide with silver cyanide and it will work pretty much well.