Can we detect exoplanets with perpendicular plane of ecliptic? If I understand correctly, all the current exoplanet search is based on planets transitioning the distant star.

If the plane of ecliptic of that star happens to be perpendicular to line of sight from Earth to that star - or sufficiently inclined, so that orbits of all its planets as seen from Earth "circle" the star without ever transitioning it - does that mean we're completely unable to detect them?
There are (at least) three main methods to detect planets that orbit so that the orbital plane is at right angles (or thereabouts) to our line of sight.

The first of these is direct imaging. This is already responsible for the discovery of a number of planets. However, in order to be visible against the glare of their host star, the exoplanets need to be in wide orbits and be massive. It also favours the detection of giant planets around young stars, since these planets are still contracting, are still warm, and emitting their own infrared light. A list of about 20 directly imaged exoplanets can be found here; arguably some of these should more rightly be called brown dwarfs.

A second method is the so-called astrometric detection of exoplanets. This works because the star and planet orbit their common centre of mass. This means that the star executes an orbit with the same period as the exoplanet, but with a semi-major axis that is smaller by the ratio of the planet mass to the star mass. This motion of the star can be detected, in a similar way to which parallax is measured, by precise measurement of position with respect to background objects. The method is most sensitive to wider binaries and massive stars, but is limited by the requirement to see appreciable motion of the star within the duration of the observational dataset. In practice then, this means it is difficult to detect planets with orbital periods of decades, unless one is prepared to wait for some time!

There may only be one accepted exoplanet discovery by this method so far (HD 176051b), but the Gaia satellite should be capable of detecting many thousands of exoplanets with masses at or above that of Jupiter and with orbital radii of about 1--10 au (see Perryman et al. 2004).

Thirdly, gravitational microlensing is quite insensitive to the plane of the orbit. This works when a foreground object gravitationally lenses and magnifies the light from a background star. An exoplanet is marked by a "blip" in the lensed light curve. There are also about 20 planets detected by microlensing. The disadvantage of this technique is that the event is a non-repeatable one-off, so not much more can be learned about these systems.

Notably, all three of these techniques are less sensitive to planets that have small mass (as indeed are transit experiments and the radial velocity technique). However, whilst small planets (in terms of mass) have been found by microlensing, it seems unlikely that the other two techniques will discover Earth-like planets for quite some time.