OpenStreetMap data is, as the name says, open data provided under an open license, there is no need to trace over a map to extract the data.
If you simply want to get the geometry of a small number of roads you could for example use http://overpass-turbo.eu/ to extract the geometry in geoJSON or other formats. AFAIK CartoDB supports OSM format data in some form directly so likely you don't even have to do that.
Currently there is no (IMHO) reasonable way to directly do what you want, so it would likely boil down to:
- exporting the required road segments to an editable format (kml, gpx, geoJSON)
- trimming to the exact length you want
- importing in to CartoDB
There are at least a dozen variants how you could do this. For example besides what I've already outlined you could simply download the area in JOSM, merge/split the road in question till it has the reuired length and then export as GPX, but they are likely all goign to will require you to learn something about the OSM data format and available tools.