Rejoice For You Are True
To requisition items from the Inquisition, it will follow the same basic rule structure as obtaining an item from the a contact from P. 222 of the Inq. Handbook, with several modifications.
A requisition is essentially putting an order in for the Inquisition to locate the item at its armory, or in the rarer cases, at the armories of the Imperial Guard or other Imperial bodies. The more rare the item is, the more expensive the initial requisition cost will be, as the Inquisition is forced to scour various planetary and sector storerooms, and transport it back to the base at which you are stationed.
Further, there is no guarantee of success, as you pay before the inquiry test takes place, and if the Inquisition is unable to locate the weapon you are out of luck. The bureaucracy and size of the Imperium is staggering, and it is easy to have items lost or even stolen in transit between planets.
To successfully requisition an item, the GM will roll an inquiry test as the Inquisition at a base skill level of 40. This may be modified upwards or downwards depending on your rank (as requisitions made by higher ranked acolytes carry far more force) and the availability of the item.