Does the current in a pure capacitive circuit lead or lag the applied voltage?

Answer #1

Just remember our friend ELI the ICE man!
E is voltage, I is current, L is inductance, and C is capacitance.
ELI
In an inductively reactive circuit (L), the voltage (E) comes first, then the current (I) lags behind.
ICE
In a capacitively reactive circuit (C), the current (I) leads, then the voltage (E) comes later.

Note that while your assumption (in the stated question) is correct, an engineer or electrician would not say it that way. The voltage waveform is the constant, and the current waveform is said to lead or lag. This is because reactive or non-linear loads distort the current. If you look at a power-factor meter, and it says leading or lagging, it is referring to the current. It would be more accurate to re-phrase your question: In a capacitive reactive circuit does the current lead the voltage? Yes!

Answer #2:

Another method I learned from one of my EE professor is that in an inductor the current lags the voltage because the electrons get dizzy going through all of those loops (coils) in the inductor and "lag" behind the voltage.