Yes, you can use a computer monitor, IF it has a HDMI and has HDCP support. If you just want to activate a Roku, the HDCP may not be needed. Most commercial channels probably require HDCP, (High Definition Copy Protection).
I use an 8 year old 24" ViewSonic 1080p monitor with one of my Rokus.
I use a KVM switch for 2 desktop PCs connected to 1 computer monitor. My 2011 Dell 21.5" monitor has 2 video inputs. The Dell monitor Input Source is set on AUTO so which ever system is operating gets displayed on the monitor or I can hit a key on the keyboard to switch PCs. I could also select which system to view on the monitor by using the monitor MENU 'button' (located on the monitor bezel) and selecting Input Source, and selecting which video input to use. Does your monitor have a MENU 'button' on its monitor bezel, with selectable Input Source? Does your monitor have 2 input ports?