The way I see it is you can keep it as is, and it has the interpretation that Dason mentioned just above, or you can make 11 dummy variables as hlsmith noted. X1= 1 if effective in January; 0 if not....X11= 1 if effective in November; 0 if not... December would be the base level in my example, but that's arbitrary and you might have a better reason for selecting one month as the base level in comparison to another.

The choice depends on whether or not you think the relationship is more smooth and the average is about the same for these groups, in which case you may opt to keep the current variable, again not a dummy variable. If you think the relationship needs to account for discrete changes in the means between groups, or maybe that slopes differ between the groups, then the dummy variable route may be more appropriate for you (need interaction if you want different slopes between groups).