Is there a mnemonic to study the spectrochemical series?
I would not recommend a mnemonic for the spectrochemical series for a number of reasons:


Often, it depends on both metal and ligand and coordination geometry how big a certain splitting is.
The splitting of some ligands ($\ce{NH3, H2O}$) is even dependent on the pH — even though that could sort-of be overcome by including their corresponding anions in the list.
Any mnemonic is bound to be incomplete. N-heterocyclic carbenes (NHCs) are very important ligands especially in organometallic chemistry, but they aren’t on your list.
Some ligands (e.g. $\ce{NO}$) can display very complex redox chemistry that defies them being ordered in a simple list.
Rather than learning some list off by heart and rote memorising it later, it is much better to know why a ligand is strong- or weak-field and to deduce that property from the ligand’s structure.


The last point is most important. Rather than learning or attempting to remember that chloride is a weak-field ligand, ask yourself why. It is a &#x3c0; donor ligand that will split the $\mathrm{t_{2g}}$ orbitals of the central metal in a bonding–antibonding way, lifting the metal’s $\mathrm{t_{2g}}$ orbitals and lowering the energy difference. That way, I immediately know what to expect of (say) selenide $\ce{Se^2-}$ even if it is not present in the list. The strength of a certain ligand in this discussion is equivalent to the usual trends in the periodic table. Quickly memorised, no long mnemonic and applicable even to new ligands.