Reduction of Earth's rotation due to increase in humidity I came to know that, moon is moving away from earth, resulting reduction of Earth's rotation. Similarly, if Earth's humidity increases, water vapor will be move up to the air from water sources, will that cause a reduction in rotation of earth speed?
 A: The short answer is, yes.
The slightly longer, but slightly more accurate answer is yes, but not noticeably.
As you say, increasing humidity by evaporating existing water will cause the mass of the vapor to move to a greater distance from the earth's center, and this will increase the moment of inertia, reducing the rotation rate.
Consider that the density of saturated water vapor at STP is about 17 g/$m^3$. With a surface area of 510 million square km, a column of saturated water vapor 2 km high at 100% RH will have a total mass of 1.7 x $10^{18}$ kg. Assuming an earth radius of 6371 km, at sea level this amount of liquid water will have a moment of inertia $mr^2$, or 70.3555 x $10^{24}$ kg $km^2$. Raising this to the effective 1 km height of the vapor ring gives a moment of inertia of 70.3777 x $10^{24}$ kg $km^2$, for a net gain of 22 x $10^{19}$ kg $km^2$. While this might seem a fair amount, you need to keep in mind that the earth's moment of inertia is about 8 x $10^{37}$ kg $km^2$.
This means that such an increase in humidity would increase the period of rotation by (roughly) a factor of 3 x $10^{-18}$, or 10 nsec / year. 
Like I say, not noticeably.  
A: This is not a simple problem. The interactions of the earth's atmospheric fluctuations and the rotational patterns are a matter of research:

Atmospheric loads (= air pressure), e.g. during a high pressure weather system, can change the shape of the elastic Earth by up to two centimetres and can also alter the Earth's gravitational force.

In this wikipedia article on "day length fluctuations"

The length of the day, which has increased over the long term of Earth's history due to tidal effects, is also subject to change on a shorter scale of time. Exact measurements of time by atomic clocks and satellite laser ranging have revealed that the length of day (LOD) is subject to a number of different fluctuations. These tiny fluctuations have periods which range from a few weeks to a few years. They are attributed to interactions between the dynamic atmosphere and Earth itself.

Thus it is not a well defined question because raising the humidity could have a different effect depending where this happens, (think interplay of cold front with humidity resulting in snow)  that is why the talk is about fluctuations on the rotation.

Crustal movements (such as continental drift) or polar cap melting are slow secular events. The characteristic coupling time between core and mantle has been estimated to be on the order of ten years, and the so-called 'decade fluctuations' of Earth's rotation rate are thought to result from fluctuations within the core, transferred to the mantle.1 The length of day (LOD) varies significantly even for time scales from a few years down to weeks (Figure), and the observed fluctuations in the LOD - after eliminating the effects of external torques - are a direct consequence of the action of internal torques. These short term fluctuations are very probably generated by the interaction between the solid Earth and the atmosphere.



Deviation of day length from SI based day, 1962–2015
A comparison between AtmosphericAangularMomentum and LenthOfDay shows that they are highly correlated. In particular, one recognizes an annual period of LOD with an amplitude of 0.34 milliseconds, maximizing on February 3, and a semiannual period with an amplitude of 0.29 milliseconds, maximizing on May 8,[4] as well as 10 day fluctuations of the order of 0.1 milliseconds. Interseasonal fluctuations reflecting El Niño events and quasi-biennial oscillations have also been observed.[5] There is now general agreement that most of the changes in LOD on time scales from weeks to a few years are excited by changes in AAM.[6]

So, depending on the AAM fluctuations the signs can be both positive and negative, i.e. increase or decrease of rotation.
Now if just one has a sphere  and changes the density and the volume of a hypothetical atmosphere on a planet that has no weather or climate, increasing its mass will increase the AAM and thus give a negative LOD, but this has nothing to do with the real earth.
