Is one allowed to pick up a cellphone on shabbos so one can see the time or is one not allowed to move it at all?
One should not do this in general, though there is room for leniency where necessary.
It is hard to consider a cellphone muktzeh machmas chisaron kis, because one does not generally designate a special place for it, and it is moved around freely. Rather, it is a keli shemelachto le-issur, because its primary use is for a prohibited purpose (based on Biur Halachah 308:3, citing from Peri Megadim).
Some dispute this and rule that a minority use is sufficient to permit the muktzeh prohibition. In addition, there is room to argue that the function of a cellphone to tell the time (and as an alarm clock) is a central enough function to permit its use on Shabbos. Even if it is muktzeh as a keli shemelachto le-issur, it will be permitted to move it for purposes of telling the time.
Yet, authorities general prohibit the moving of a cellphone on Shabbos, both because of the zilzul involved in this, and because of the changes on the display that take place when the phone is moved. See also Orchos Shabbos 19:44, and footnote.