Just possibly, maybe, but not easily.
Ocean movement due to tides is mostly back-and-forth with mixing. It can be very complicated around barriers and in estuaries and the entrance to bays and places like that. In the deep ocean near the surface the motion of any given bit of water is more-or-less circular during a cycle of the tides.
Don't forget that the pulls involved in producing tides are cyclic, and pull "back" as often as "forward." So which way do you expect the sustained flow to be?
Ocean currents are driven by wind, salinity differences, temperature differences, and gravity. And occasionally earthquakes. This is how you can sustain flow in a direction. For example, consider where a fresh water river enters the ocean. This introduces non-salty water at a different temperature. This will tend to flow steadily in a direction determined by the various surrounding details. Or consider the existence of trade winds that blow in one direction much more of the time than any other. This will tend to drive surface water in that direction, returning it along some other flow path.
So the usual naturally occurring situation will not mean tides produce a sustained flow in one direction around the equator. You would have to construct something extremely contrived. Imagine, for example, a sequence of bays just angled perfectly to produce very high tides such that water flows up and over some barrier on one side. But the shape of the ocean shore on the other side did not produce such high tides. You'd need to "focus" the shape of the bay on one side, say the west side, to amplify the tides. Then at only the high point of the tide it spills over the edge, and only in one direction. You'd need a whole series of such all around the equator to produce anything like a sustained flow. Note that they would not need to be above the surface of the ocean, only close enough to the surface to focus the tidal flow in this manner.
Maybe a little like that. From one side, each terrace tends to collect the flow inward to the center. From the other it tends to disperse it. So the first half of the daily tide cycle gets pushed in, and the second half gets pushed out. If you had a series of these all the way around the equator, the water would tend to flow west-to-east in the middle, and east-to-west along the top and bottom of the terrace. Note that to work they would have to be many 100 km long, and there would have to be a lot of them, probably all the way around the equator. Plus they'd have to be spaced just the right distance apart.
So a wild idea of how that might have happened. Maybe many centuries ago the water level was much lower. An ice age perhaps? And the land at the equator was above the ocean. And the people who lived there then did a lot of terracing and shaped the land all the way around the equator to produce good growing. Maybe something like rice that wants to grow in water some of the time? Maybe they faced all these terraces towards the east so they got the morning sun. And the shape of all these artificially constructed hills is just perfect to focus the tides.