The poetry of Emily Dickinson commonly included reference to the color purple. Purple has many different meanings when used in a work. It can represent a balance given purple is created by using red (the warmest color) and blue (the coolest color). It can also represent nobility and spirituality (think the garb worn by both kings and priests). Naturalistically, purple is the color of many flowers which are considered both precious and frail. Lastly, the color purple is associated with mourning.
As for the use of the color purple in Dickinson's poem "As if I asked a common alms", one must first define any words which may cause confusion for you as a reader.
Alms- donations given to the poor (typically food or money)
Morn- the period of time denoted as existing between dawn and noon
Dike- either a waterway, a bank used to confine water, or a barrier which prevents the passage of something deemed undesirable.
This terms being defined allow for a more understandable position on the poem. A common theme of the poem is spirituality and hope as denoted by the terms 'alms', 'Kingdom', and 'asked.'
As for the use or meaning of the color purple, it could be understood to represent the hope (based upon spirituality) that all questions will be answered once dawn (symbolizing enlightening) breaks as the dike (symbolizing darkness) is lifted. The description of the dike being purple shows what must be changed in the scheme of things so as to bring the answers to the questions the speaker so vehemently needs.