You could asked Globe to replace your sim with a micro-sim, just go to the nearest Globe Business Center. (Might have a fee)
Manually cut your old sim to became a mirco-sim. Just google for the layout/guide.
Naks! Naka iphone na! #BigyanNgJacket
Aside from the useful tips that @notevenfollowed gave you, in case you find the lines in Globe stores too long and you are not brave enough to cut your own sim, you can also go to many cellphone stores, stalls that you can find in malls, shopping centers, Divisoria and Quiapo and I'm sure that many of them have sim cutters. They will charge you from P40 to P100 depending on how you look.
Be sure to keep the portion that was cut off so you can use it to frame your newly cut microsim in case you want to use it with a regular simmed phone. If it has been destroyed, you can always buy in CDRKing.