EMB-135LR Captain reported encountering wake turbulence departing PHX in trail of a B737 NG that resulted in a slight track deviation.

Narrative

[We were] cleared for takeoff on Runway 25R following a departure by a Boeing 737; which was to diverge to the south. The takeoff was executed as briefed and by standard operating procedure (SOP) callouts. Additionally; the flight mode annunciator (FMA) was confirmed as having LNAV armed prior to taking Runway 25R. At approximately 300 feet; we had a brief wake turbulence encounter which rolled the airplane left. I rolled wings level and side-stepped slightly to the right; outside of the preceding aircraft's planned turn and increased our climb rate to avoid further wake encounters. Due to the encounter; roll correction; and side-step; the flight management system (FMS) failed to engage at 400 feet and to capture and proceed to JINOL; the first named waypoint on the MRBIL1 Departure and remained in heading mode. The map on the multi-function display (MFD) showed a course line labeled with 'Vectors' after JINOL. I called for FO to program direct to the OSGUE waypoint; which he did. The correction following the wake encounter and the avoidance maneuver took us to a point 0.3 miles to the north of course before I turned back to the south once we were clear of the wake turbulence threat. No further wake encounters occurred. Air traffic control (ATC) did not inquire about the maneuver or ensuing brief change in course. At no point was the safety of the departure in question.The cause of this incident was encountering wake turbulence after takeoff; taking measures to avoid additional wake turbulence; and failure of the FMS to capture the waypoint upon passing 400 feet AGL following the abrupt disruption in attitude.There are three recommendations to avoid this situation in the future. First; taking measures to avoid the potential wake turbulence situations by asking for a delay prior to being cleared for takeoff to provide more in-trail spacing between our aircraft and the preceding departing traffic. Second; ATC could have issued a cautionary advisory for wake turbulence with latitude to offset. Lastly; the FMS should be programmed to acquire and stay locked onto the follow-on waypoint regardless of any abrupt disruptions in attitude or aircraft proximity to the prior waypoint.